4A

This page contains lecture videos for PHYC 4A, as part of the comprehensive 4-series lecture video project.

The html source for this outline can be downloaded by following the link below (you may need to rename the file to ".htm" to get it to work on your computer):

• basic html outline page

• Classical Mechanics (from project and 2A) (91:04:01)

  • How physics relates to other fields of study (50:36)

    • The heirarchy of science (16:41)
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    • The game of life (https://playgameoflife.com) (17:30)
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    • Math versus science (16:25)
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  • Units (1:45:16)

    • Measured quantities (9:54)
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    • Systems of units (12:24)
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    • Historical and present-day definitions of SI units (20:58)
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    • Conversion factors and unit prefixes (9:48)
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    • Units conversion example (22:13)
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    • Units raised to a power (5:57)
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    • Example: painting a wall (9:53)
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    • Basic dimensional analysis (14:09)
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  • Vectors (10:19:06)

    • Basic properties (2:47:33)

      • Vectors vs. scalars (8:26)
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      • The displacement vector (12:22)
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      • General vectors (9:02)
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      • Adding displacement vectors (14:21)
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      • Adding vectors in general (12:18)
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      • Subtracting vectors (9:23)
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      • Components in two dimensions (9:44)
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      • Components as vectors / three dimensions (18:12)
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      • Magnitude and direction to components (14:36)
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      • Components to magnitude and direction (13:05)
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      • Adding and subtracting vectors using components (10:14)
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      • Example: adding vectors (21:28)
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      • Example: subtracting vectors (7:17)
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      • Multiplying a vector by a scalar (7:05)
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    • Products of vectors (2:09:08)

      • The dot product: definition and basic properties (13:18)
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      • Parallel and perpendicular components (11:45)
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      • The cross product: definition and basic properties (21:26)
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      • Example: evaluating the cross product (7:03)
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      • Geometric tricks: law of cosines and law of sines (13:33)
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      • Geometric tricks: angle between vectors (10:02)
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      • Geometric tricks: areas and volumes (12:54)
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      • Triple product identities (9:08)
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      • Triple product identities: derivation 1 (10:04)
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      • Triple product identities: derivation 2 (19:55)
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    • Alternative coordinate systems (2:11:41)

      • Introduction (3:24)
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      • Polar coordinates (2D) (16:13)
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      • Specifying direction in 2D: an alternate method (12:24)
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      • Cylindrical coordinates (3D) (10:25)
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      • Spherical coordinates (3D) (17:13)
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      • Specifying direction in 3D (19:45)
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      • Specifying direction with unit vectors (7:58)
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      • Polar coordinate unit vectors (19:20)
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      • Cylindrical and spherical coordinate unit vectors (24:59)
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    • Length of day (an application of spherical coordinates) (3:10:44)

      • Introduction (26:37)
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      • Coordinate systems (15:30)
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      • Day-night parameter (25:50)
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      • Noon (23:56)
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      • Length of day (20:52)
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      • 24 hour days and nights (27:28)
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      • Sidereal vs. solar days (21:17)
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      • Variation in length of solar day (29:14)
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  • Kinematics in one dimension (6:51:39)

    • Basic definitions (1:21:26)

      • Introduction (3:01)
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      • Position (8:35)
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      • Displacement (12:06)
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      • Average speed and velocity (13:37)
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      • Instantaneous speed and velocity (12:59)
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      • Acceleration (17:33)
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      • Speeding up vs. slowing down (13:35)
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    • Representations of motion (1:43:44)

      • Motion diagrams (14:30)
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      • Plotting graphs of motion (13:02)
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      • Using slope to calculate velocity (11:42)
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      • Relating graphs and motion (9:59)
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      • Calculating motion based on algebraic formula for position (8:27)
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      • Example (21:48)
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      • Acceleration to velocity to position using integrals (13:01)
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      • Average velocity revisited (11:15)
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    • Constant acceleration (1:27:06)

      • Introduction (21:08)
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      • Derivation 1 (algebraic) (8:21)
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      • Derivation 2 (calculus) (7:16)
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      • Example: Boat (8:31)
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      • General time interval (11:49)
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      • Example: Car (18:50)
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      • Example (multiple interval): sprinter (11:11)
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    • Vertical free-fall (2:00:23)

      • Introduction (24:07)
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      • Example (25:47)
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      • Example: rock dropped into a hole (1:10:29)

        • Simplified version (5:49)
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        • Full problem setup (10:13)
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        • Iterative solution (15:07)
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        • Analytic solution (12:01)
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        • Physical interpretation of the second solution (13:20)
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        • Epilog: some comments on quadratic equations (13:59)
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    • Quantity vs. change in quantity vs. average quantity (19:00)
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  • Kinematics in two and three dimensions (6:45:36)

    • Basic relationships (2:46:30)

      • Position in two and three dimensions (10:25)
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      • Redefining other kinematic variables in two and three dimensions (11:42)
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      • Calculus relationships (14:30)
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      • Example (19:05)
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      • Velocity direction (5:30)
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      • Acceleration vs velocity: speeding up, slowing down, changing direction (1:45:18)

        • Velocity-acceleration relationship (20:14)
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        • Geometric argument (14:32)
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        • Parametric description of a (curved) path (13:01)
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        • Incremental displacement along a path (8:09)
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        • The unit tangent vector (14:16)
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        • The curvature vector (20:13)
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        • Mathematical derivation of the velocity-acceleration relationship (14:53)
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    • Projectile motion (1:32:37)

      • Constant acceleration (2D/3D) (5:01)
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      • Projectile motion (general discussion) (12:45)
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      • Example: cannon 1 (13:26)
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      • Example: cannon 2 (17:28)
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      • Range formula (16:42)
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      • Example: horizontal launch (10:11)
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      • Example: horizontal launch, tilted floor (17:04)
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    • Uniform circular motion (54:40)

      • Introduction (5:19)
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      • Geometric argument (10:48)
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      • Calculus derivation (12:15)
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      • Example: race track (6:05)
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      • Example: satellite orbitting the earth (7:24)
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      • General circular motion (12:49)
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    • Relative motion (1:31:49)

      • Introductory example (2:50)
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      • Relative motion relationships (19:39)
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      • Introductory example revisited (18:55)
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      • Example: boat in water (12:34)
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      • Example: walking on a speed ramp (8:38)
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      • Example: airplane flying through air (14:52)
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      • Example: rain falling as viewed by moving train (14:21)
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  • Forces and Newton's laws (28:42:04)

    • Newton's laws (1:10:15)

      • Introduction (10:34)
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      • Newton's first law (9:14)
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      • Newton's second law (41:36)

        • Direction (12:21)
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        • Magnitude (11:54)
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        • 1-D example (11:44)
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        • 2-D example (5:37)
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      • Newton's third law (8:51)
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    • Force laws (1:56:01)

      • Gravity (12:27)
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      • Gravity: weighing an object (17:11)
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      • Normal force (8:22)
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      • Normal force: comparison to Archimedes' Principle (16:56)
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      • Tension (10:14)
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      • Tension: Newton's third law (13:02)
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      • Friction demos (5:57)
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      • Friction (15:26)
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      • Friction: atomic model (16:26)
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    • Force problems (3:58:39)

      • Methodology (8:06)
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      • Hanging block (27:27)

        • Block hanging from ceiling (zero acceleration) (15:48)
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        • Hanging block: non-zero acceleration (11:39)
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      • Block on floor (angled push) (56:09)

        • No friction (21:42)
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        • Kinetic friction (16:03)
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        • Static friction (18:24)
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      • Two horizontal forces on block (2-D example) revisited (23:38)
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      • Block pushed against vertical wall (21:32)
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      • Block on incline plane (1:14:55)

        • No friction (setup) (10:30)
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        • Components of gravity using tilted coordinate system (10:12)
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        • No friction (completion) (16:37)
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        • Static friction (15:56)
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        • Kinetic friction (14:21)
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        • Solving no friction case with untilted coordinate system (7:19)
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      • Static friction between tires and road for accelerating car (26:52)
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    • Multiple objects (5:09:07)

      • Two hanging blocks (16:38)
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      • Stacked blocks (18:08)
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      • Sliding block connected to hanging block (1:22:43)

        • Horizontal table, static friction (17:17)
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        • Horizontal table, kinetic friction (part 1) (15:30)
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        • Horizontal table, kinetic friction (part 2) (19:11)
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        • Inclined table (18:30)
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        • Two pulley setup (mechanical advantage) (12:15)
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      • Stacked blocks, horizontal force on top block (1:27:30)

        • Static friction between blocks (23:41)
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        • Kinetic friction between blocks (18:21)
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        • Friction at both surfaces: general force problem (18:31)
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        • Friction at both surfaces: specific cases (26:57)
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      • Block sliding down a movable incline (1:44:08)

        • Kinematics (17:54)
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        • Applying Newton's second law (15:02)
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        • Solving the equations (26:25)
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        • Some additional relationships (16:15)
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        • Checking limiting cases (28:32)
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    • Circular motion (3:04:34)

      • Introduction (10:28)
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      • Block on a string (31:47)

        • Block supported by floor (12:04)
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        • Block in midair (7:08)
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        • Numerical example (12:35)
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      • Car rounding a bend (1:11:39)

        • Unbanked with friction (17:44)
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        • Banked without friction (14:05)
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        • A math trick involving trig functions (14:26)
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        • Banked with friction (25:24)
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      • Vertical circles (21:32)
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      • Normal force on curved surfaces (49:08)

        • Qualitative discussion (8:03)
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        • Calculation setup (10:03)
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        • Calculation (12:36)
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        • Dome example (8:36)
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        • Dome example: derivation of speed (9:50)
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    • Non-inertial reference frames (1:58:07)

      • Modified Newton's second law (13:08)
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      • Real world examples (58:14)

        • Vertically accelerating elevator (12:17)
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        • Accelerating car (15:56)
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        • Circular motion (15:17)
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        • Experiencing weight: volume vs contact force (14:44)
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      • Force problems in non-inertial reference frames (46:45)

        • Projectile motion in an accelerating elevator (17:05)
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        • Block hanging from a ceiling of an accelerating car (15:43)
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        • Banked curve with friction revisited (13:57)
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    • Position and velocity dependent forces (7:38:04)

      • Classification of forces (10:50)
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      • Force problem scenarios (19:17)
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      • Spring force (53:22)

        • Hooke's law (17:29)
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        • Vertical hanging spring (16:30)
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        • Block on incline held by rope (ambiguous) (6:44)
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        • Block on incline held by spring (unambiguous) (12:39)
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      • Inverse square forces (1:01:13)

        • Force law (13:33)
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        • Planetary gravity (18:01)
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        • Two charges connected by a spring (equilibrium) (13:31)
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        • Two charges connected by a spring (equilibrium): numerical solution (16:08)
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      • Drag (fluid resistance) forces (2:22:43)

        • Linear and quadratic models (10:30)
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        • Reynolds number (8:58)
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        • Terminal velocity (50:24)

          • Qualitative discussion (8:17)
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          • Calculating terminal velocity (17:04)
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          • Correcting for buoyancy (11:49)
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          • Example: iron sphere (13:14)
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        • Model discussion (1:12:51)

          • A simple model for linear drag (14:50)
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          • A simple (and misleading) model for quadratic drag (19:40)
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          • Embedding the linear model within the quadratic model (7:37)
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          • Drag coefficient vs Reynolds number for a sphere (10:06)
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          • Calculating terminal velocity revisited (20:38)
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      • General solution methods (2:50:39)

        • Newton's second law as a differential equation (20:11)
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        • Spring-mass oscillations (23:08)
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        • Fall from rest: linear air resistance (23:12)
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        • Separation of variables for math purists (9:47)
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        • Fall from rest: quadratic air resistance (8:41)
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        • Other situations involving air resistance (9:56)
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        • Numerical methods (17:59)
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        • Spring-mass oscillations (spreadsheet) (32:40)
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        • 2-D kinetic friction example revisited (spreadsheet) (25:05)
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    • Dimensional analysis (3:47:17)

      • Limitations imposed by dimensional onsistency (56:16)

        • Setup (9:17)
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        • Allowed mathematical operations (11:11)
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        • Equation structure (23:16)
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        • Scaling laws (12:32)
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      • Nondimensionalization (1:46:14)

        • Introduction (8:12)
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        • Spring-mass oscillations (23:58)
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        • Fall from rest: linear air resistance (17:26)
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        • Fall from rest: quadratic air resistance (12:35)
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        • Fluid flow: setup (15:19)
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        • Fluid flow (28:44)
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      • The role of units in the laws of physics (1:04:47)

        • The 'constants' of nature (16:21)
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        • What SI units say about us and our experiences (21:35)
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        • What planck units say about the fundamental laws of physics (18:12)
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        • Deriving planck units (8:39)
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  • Systems of particles (8:39:43)

    • Introduction (9:41)
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    • Center of mass (4:16:12)

      • Definition (7:52)
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      • 2-D example (5:54)
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      • Continuous distributions (3:38:47)

        • Introduction (8:10)
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        • Example: 1-D uniform rod (11:15)
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        • Example: 1-D non-uniform rod (10:00)
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        • Example: 2-D non-uniform rectangle (22:04)
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        • Example: 2-D uniform triangle (16:37)
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        • General parameterizations (2:30:41)

          • 1-D curves: parameterization and line element (13:51)
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          • 2-D surface: parameterization (10:47)
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          • 2-D surface: surface element (23:26)
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          • 3-D region: parameterization and volume element (12:13)
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          • Example: uniform semi-circular rod (14:07)
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          • Example: uniform semi-circular disk (16:56)
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          • Example: uniform hemi-spherical surface (13:13)
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          • Example: uniform hemi-spherical volume (10:00)
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          • Cartesian, cylindrical, and spherical coordinate systems (13:15)
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          • Example: uniform triangle (22:53)
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      • Partition theorem (11:34)
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      • Objects with holes (12:05)
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    • Newton's second law for systems (1:57:03)

      • Derivation (14:30)
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      • Projectile examples (13:23)
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      • Two blocks moving in tandem (15:20)
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      • Example: skaters and pole (14:05)
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      • Example: person in a boat (18:28)
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      • Example: two masses connected by spring 1 (solution) (18:34)
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      • Example: two masses connected by spring 2 (force diagrams) (22:43)
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    • Two object systems (1:42:31)

      • Kinematics (12:04)
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      • Newton's second law with reduced mass (12:26)
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      • Motions of individual particles (10:26)
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      • Example: two heavenly bodies orbitting each other (17:40)
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      • Example: spring-mass oscillations with two masses (12:03)
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      • Previous spring-masses problem revisited (22:48)
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      • Non-isolated two object systems (15:04)
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    • Newton's third law and indirect interactions (34:16)

      • Indirect interactions (19:01)
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      • Newton's third law (15:15)
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  • Conservation laws (2:02:21)

    • General discussion and examples (1:12:33)

      • Introduction (4:05)
        m4v / mp4

      • Conservation of volume (14:23)
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      • Conservation of charge (6:51)
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      • Universal vs. non-universal conservation principles (8:56)
        m4v / mp4 / page-1

      • Various particle number conservation principles (25:34)
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      • Global vs. local conservation principles (12:44)
        m4v / mp4 / page-1

    • Momentum and energy (49:48)

      • Definition of momentum and kinetic energy (7:32)
        m4v / mp4 / page-1

      • Momentum and energy conservation (11:41)
        m4v / mp4 / page-1

      • Impulse and work (9:46)
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      • Example (6:41)
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      • Example continued (14:08)
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  • Impulse and Momentum (from 2A) (2:27:23)

    • Impulse-Momentum theorem (1:03:32)

      • Impulse-momentum theorem (9:33)
        m4v / mp4 / page-1

      • Impulse (10:45)
        m4v / mp4 / page-1

      • Momentum (12:40)
        m4v / mp4 / page-1

      • Baseball example (1-D) (16:23)
        m4v / mp4 / page-1

      • Baseball example (2-D) (14:11)
        m4v / mp4 / page-1

    • Conservation of momentum (1:23:51)

      • Conservation of momentum (15:58)
        m4v / mp4 / page-1

      • Car example 1 (15:18)
        m4v / mp4 / page-1

      • Car example 2 (13:18)
        m4v / mp4 / page-1

      • Elastic vs. inelastic collisions (13:11)
        m4v / mp4 / page-1

      • Elastic collisions in 1-D (18:48)
        m4v / mp4 / page-1

      • Recoil (7:18)
        m4v / mp4 / page-1

  • Work and Energy (from 2A) (4:30:16)

    • Kinetic Energy (2:36:36)

      • Energy introduction (3:18)
        m4v / mp4

      • Kinetic energy (8:13)
        m4v / mp4 / page-1

      • Work (20:09)
        m4v / mp4 / page-1 / page-2

      • Work done by 1-D constant force (7:29)
        m4v / mp4 / page-1

      • Single force example (15:28)
        m4v / mp4 / page-1

      • Multiple force example (11:28)
        m4v / mp4 / page-1

      • Work done by 3-D constant force (12:56)
        m4v / mp4 / page-1

      • Example (13:36)
        m4v / mp4 / page-1

      • Work done by gravity (19:41)
        m4v / mp4 / page-1

      • Work done by normal (and tension) force (21:29)
        m4v / mp4 / page-1 / page-2

      • Work done by (kinetic) friction (12:27)
        m4v / mp4 / page-1

      • Work done by lift force (10:22)
        m4v / mp4 / page-1

    • Potential and Mechanical Energy (1:53:40)

      • Conservative and non-conservative forces (11:35)
        m4v / mp4 / page-1

      • Potential energy (14:20)
        m4v / mp4 / page-1

      • Gravitational potential energy (13:54)
        m4v / mp4 / page-1 / page-2

      • Mechanical energy (13:52)
        m4v / mp4 / page-1 / page-2

      • Example: free-fall (12:13)
        m4v / mp4 / page-1

      • Example: pendulum (23:41)
        m4v / mp4 / page-1 / page-2

      • Example: lift force revisited (7:40)
        m4v / mp4 / page-1

      • Example: slide with friction at the bottom (16:25)
        m4v / mp4 / page-1 / page-2

  • Rotational Kinematics (from 2A) (2:15:14)

    • Basic definitions (58:57)

      • Rotation introduction (5:42)
        m4v / mp4 / page-1

      • Angular position (16:13)
        m4v / mp4 / page-1

      • Angular displacement (7:20)
        m4v / mp4 / page-1

      • Angular velocity (6:16)
        m4v / mp4 / page-1

      • Angular acceleration (9:12)
        m4v / mp4 / page-1

      • Constant angular acceleration (14:14)
        m4v / mp4 / page-1 / comments

    • Motion of particles in a rotating object (54:54)

      • Particle distance (11:38)
        m4v / mp4 / page-1

      • Particle velocity (13:09)
        m4v / mp4 / page-1

      • Particle acceleration (16:37)
        m4v / mp4 / page-1 / page-2

      • Tennis serve example (13:30)
        m4v / mp4 / page-1

    • Rolling motion (21:23)

      • Rolling without slipping (13:27)
        m4v / mp4 / page-1

      • Rolling example (7:56)
        m4v / mp4 / page-1

  • Rotational Dynamics (from 2A) (4:53:04)

    • Torque and rotational inertia (1:35:06)

      • Translation-rotation analogy -- Newton's Second Law (15:36)
        m4v / mp4 / page-1

      • Torque: definition (18:39)
        m4v / mp4 / page-1

      • Torque: example (21:35)
        m4v / mp4 / page-1

      • Rotational inertial: definition (15:03)
        m4v / mp4 / page-1

      • Rotational inertia of shapes (24:13)
        m4v / mp4 / page-1

    • Applications of Newton's second law for rotation (1:56:04)

      • Example: revolving door (18:27)
        m4v / mp4 / page-1

      • Example: falling rod (23:25)
        m4v / mp4 / page-1

      • Conditions for static equilibrium (7:57)
        m4v / mp4 / page-1

      • Balancing a rod with attached weights (31:22)
        m4v / mp4 / page-1 / page-2

      • Leg example (34:53)
        m4v / mp4 / page-1 / page-2

    • Rotational energy (1:21:54)

      • Rotational work and kinetic energy (13:44)
        m4v / mp4 / page-1

      • Rotational example (includes rolling) (19:11)
        m4v / mp4 / page-1 / page-2

      • Rolling down an incline (19:34)
        m4v / mp4 / page-1

      • Static friction and rolling uphill (29:25)
        m4v / mp4 / page-1 / page-2

  • Fluids (from 2A) (3:49:02)

    • Introduction (36:33)

      • Fluid introduction (8:14)
        m4v / mp4 / page-1

      • Density (11:48)
        m4v / mp4 / page-1

      • Pressure (16:31)
        m4v / mp4 / page-1

    • Static fluids (1:42:26)

      • How pressure depends on depth (15:38)
        m4v / mp4 / page-1

      • Examples: Swimming pools, U-tubes, and straws (29:57)
        m4v / mp4 / page-1 / page-2

      • Pascal's principle (20:48)
        m4v / mp4 / page-1 / page-2

      • Archimedes' principle (20:59)
        m4v / mp4 / page-1 / page-2

      • Example 1: ice in water (6:20)
        m4v / mp4 / page-1

      • Example 2: iron in water (apparent weight) (8:44)
        m4v / mp4 / page-1

    • Moving fluids (1:30:03)

      • Assumptions (14:08)
        m4v / mp4 / page-1

      • Streamlines (11:38)
        m4v / mp4 / page-1

      • Flowrates (15:50)
        m4v / mp4 / page-1

      • How pressure depends on speed in a horizontal pipe (13:58)
        m4v / mp4 / page-1

      • Bernouli's equation (18:13)
        m4v / mp4 / page-1 / page-2

      • Draining water tank example (16:16)
        m4v / mp4 / page-1

  • Systems with one degree of freedom (from pre-2020 videos) (7:12:41)

    • Definition and examples (23:39)
      m4v / mp4 / page-1 / page-2 / page-3

    • Generalized position, velocity, and acceleration (14:34)
      m4v / mp4 / page-1 / page-2

    • Relating generalized quantities to the motion of various parts of the system (25:24)
      m4v / mp4 / page-1 / page-2 / page-3

    • Derivation of Newton's 2nd Law (1-D translation) from the Work-Energy Theorem (11:23)
      m4v / mp4 / page-1 / page-2

    • Generalization of Newton's 2nd Law --- application to translation and rotation (26:42)
      m4v / mp4 / page-1 / page-2 / page-3

    • Example: Two masses connected by a rope over a pulley (32:38)
      m4v / mp4 / page-1 / page-2 / page-3

    • Example: Rolling object on an incline (24:07)
      m4v / mp4 / page-1 / page-2

    • Example: Two pulley system (mechanical advantage) (30:27)
      m4v / mp4 / page-1 / page-2

    • Example: Mechanical lever (14:09)
      m4v / mp4 / page-1 / page-2

    • Example: Gear system (common rotation) (18:16)
      m4v / mp4 / page-1 / page-2

    • Example: Gear system (common outer translational speed) (17:34)
      m4v / mp4 / page-1 / page-2

    • Example: Bicycle (36:17)
      m4v / mp4 / page-1 / page-2 / page-3

    • Some general notes on dynamics (21:48)
      m4v / mp4 / page-1 / page-2 / page-3

    • Which forces can be ignored (43:01)
      m4v / mp4 / page-1 / page-2 / page-3

    • Summary of simple spring-mass system (14:17)
      m4v / mp4 / page-1 / page-2

    • Generalized harmonic oscillations (9:59)
      m4v / mp4 / page-1 / page-2

    • Example: Spring-mass system with a massive spring (17:57)
      m4v / mp4 / page-1 / page-2

    • Example: Pendulum (7:47)
      m4v / mp4 / page-1 / page-2

    • Example: Spring attached to a rotating board (9:12)
      m4v / mp4 / page-1

    • Example: Fluid oscillations in a U-tube (11:05)
      m4v / mp4 / page-1

    • Example: Spring-mass oscillations involving the two-pulley system (mechanical advantage) (9:40)
      m4v / mp4 / page-1 / page-2

    • Epilog: Systems with more than one degree of freedom (12:47)
      m4v / mp4 / page-1 / page-2 / page-3