Mechanics
Measurement
Basic Units
To introduce the concept of mass.
To discuss units of mass and the concept of standards of mass.
To introduce the concept of length.
To discuss units of length and the concept of standards of length.
Error & Accuracy
Coordinate Systems
Vectors
To introduce the concept of time.
To model a binomial probability distribution.
1A30.30 Walking on a Rotating Platform
To demonstrate radial and angular components of motion.
To introduce students to the concept of vectors.
Scaling
To visualize the scale of the known universe.
Motion in One Dimension
Velocity
Uniform Acceleration
To demonstrate how the total velocity of a truck changes when it rolls across a moving sheet.
1C10.20 Constant Velocity Dynamic Track
To demonstrate motion with constant velocity.
1C10.25 Constant Velocity Air Track
To demonstrate motion with constant velocity in the absence of friction.
To demonstrate that in the absence of air resistance, all objects fall at the same rate.
To demonstrate constant gravitational acceleration.
1C20.30 Constant Acceleration Dynamic Track
To demonstrate motion with uniform acceleration.
1C20.35 Constant Acceleration Air Track
To demonstrate motion with uniform acceleration in the absence of friction.
To demonstrate the constant acceleration of a ball down a ramp.
Measuring Gravitational Acceleration
To measure a person’s reaction time.
To determine the gravitational acceleration experienced by a falling object.
Motion in Two Dimensions
Displacement in Two Dimensions
1D10.10 Rotating Velocity Vectors
To demonstrate vector components of angular motion.
To demonstrate that circular motion can be converted into linear motion.
To demonstrate angular and radial displacement.
1D10.50 Simple Harmonic Motion and Uniform Circular Motion
To show that simple harmonic motion is the projection of uniform circular motion.
Velocity, Position and Acceleration
To demonstrate change in position and velocity as functions of time.
1D15.20 Cycloid Generator (Simulation)
To show a point on the circumference of a rolling disk traces out a cycloid.
To show that three balls which travel down different paths in different amounts of time have the same final velocity.
To demonstrate the properties of a cycloid track.
Motion of the Center of Mass
To demonstrate that two balls released from the same height travel two different paths in the same amount of time.
To demonstrate that as a person walks across a rolling plank, the center of mass of the person/plank system remains constant.
1D40.11 Force Platform (Parallel)
To measure the parallel (shear) force compared to the center of mass motion.
To show that the center of mass of a projectile travels a parabolic path regardless of the motion of the rest of the object.
Central Forces
1D40.35 Center of Mass Between Two Objects
To show how the center of mass varies with the difference between the masses of the objects.
1D40.50 Dual Pendulum Dynamic Track
To show that as two heavy pendula swing, the system’s center of mass changes.
1D40.55 Dual Pendulum Air Track
To show that as two heavy pendula swing, the system’s center of mass changes in the absence of friction.
To demonstrate that centripetal force is directed toward the center of a circle.
To demonstrate that centripetal force and friction can overpower gravity.
To show that centripetal force prevents water from spilling out of a spinning bucket.
To demonstrate that centripetal force holds a glass of water on a tray as the tray swings in a circle.
1D50.50 Orbiting Mass on a Spring
To show centripetal force stretches a rotating spring attached to a mass.
Deformation by Central Forces
To demonstrate that a chain loop with high enough angular velocity behaves as a rigid wheel.
To demonstrate centripetal force will flatten a rapidly rotating sphere.
To show that a vortex can be formed by centripetal force.
To show that a parabolic surface is formed from rotating water in a container due to centripetal force.
Centrifugal Escape
To demonstrate centripetal force using an air bubble in a dish of water.
To demonstrate liquids of different densities can be separated by centripetal force.
To demonstrate uniform circular motion with a spinning donut.
To demonstrate a ball rolling along a ring continues tangentially when it reaches a gap.
Projectile Motion
1D55.30 Rotating Turntable and Puck
To demonstrate the forces felt by a puck at different locations on a rotating turntable.
1D60.05 Projectile Motion Ball
To demonstrate the basic principles of projectile motion.
To demonstrate the independence of horizontal and vertical components of a projectile's velocity.
To demonstrate the independence of horizontal and vertical components of the velocity of an object in free-fall.
1D60.30 Projectile and Falling Target
To demonstrate the independence of horizontal and vertical components of the velocity of a projectile fired at a falling target.
To demonstrate that the maximum projectile range is achieved at a launch angle of 45 degrees.
1D60.41 Water Parabola with Parabola Vectors
To demonstrate that projectiles follow a parabolic path.
To demonstrate the independence of horizontal and vertical components of the velocity of a billiard ball launched at a second ball in free fall.
Relative Motion
Moving Reference Frames
Rotating Reference Frames
To demonstrate how the total velocity of a truck changes when it rolls across a moving sheet.
To illustrate relative velocity using a cart on a moving track.
1E20.00 Inertial and Non-Inertial Reference Frames
To demonstrate inertial and non-inertial reference frames using a pendulum on a turntable.
1E20.10 Classroom Foucault Pendulum
To show the coriolis force of the Earth.
1E30.28 Ball on a Rotating Turntable with Ramp and Hole
To demonstrate the Coriolis force on a ball rolling on a rotating turntable.
1E30.29 Coriolis Ball on a Rotating Track
To show that a ball on a rotating track moves in a straight line in the rotating reference frame.
Newton's First Law
Measuring Inertia
Inertia of Rest
To demonstrate how mass is measured independent of gravitational forces.
To show that inertia is resistance to acceleration.
1F20.24 Daruma Otoshi (Inertia Blocks and Hammer)
To show that inertia prevents a stack of blocks from falling when the bottom block is knocked out.
To show that the inertia of a plate resists the acceleration of a table cloth pulled out from beneath it.
Inertia of Motion
To show inertia causes a block on a PVC pipe to remain in place when the PVC is struck by a mallet.
1F30.10 Constant Velocity Air Track
To demonstrate an object’s inertia keeps it in motion in the absence of friction.
1F30.11 Newton's First Law - Air Puck
To demonstrate Newton's first law of motion with a frictionless air puck.
To demonstrate the inertia of motion of a falling chain.
To show that inertia causes percussion when water strikes the end of an evacuated tube.
Newton's Second Law
Force, Mass and Acceleration
1G10.10 Constant Acceleration Air Track
To demonstrate Newton's second law in the absence of friction.
1G10.11 Newton's Second Law Dynamic Track
To demonstrate Newton's second law with a pulley and dynamic cart.
To demonstrate Newton's Second Law with a cart and a spring scale.
To demonstrate Newton's Second Law with a cinder block and a spring scale.
1G10.30 Spring Scale and Normal Force
To demonstrate that the sum of the tension and normal forces supporting a mass is always equal to the mass’s weight.
1G10.31 Force Platform - Standing and Jumping
To show the force exerted by a person's feet while they are standing on and jumping off a platform.
To show the force required to decelerate a falling chain is greater than the chain’s weight.
To demonstrate Newton's Second Law with an Atwood’s machine and unequal masses.
Accelerated Reference Frames
1G20.30 Equivalence Principle Cup on Stick
To show that the force of gravity on a body cannot be distinguished from an acceleration.
1G20.41 Freefall Spring Scale and Mass
To show an object is effectively weightless in freefall.
To demonstrate the equivalence principle with a falling Slinky.
1G20.71 Equivalence Principle Pendulum
To demonstrate that a pendulum rolling down an incline is effectively weightless.
Action and Reaction
To demonstrate Newton's Third Law with a mass and spring.
To demonstrate conservation laws and Newton's Third Law.
1H10.13 Two Carts and a Spring
To show that when a spring between two carts is compressed and released, the carts move apart with equal and opposite velocity.
To show action and reaction with a fan on a cart.
Statics of Rigid Bodies
Finding the Center of Gravity
Exceeding the Center of Gravity
To find the center of mass of an irregularly shaped object.
1J10.30 Meter Stick on Fingers
To show that balance of torques and normal force can be used to find the center of mass of an object.
1J11.15 Tipping Block on an Incline
To show that a standing block topples when its center of mass is no longer supported by its base.
To show a stack of wooden blocks hanging off the edge of a table is stable as long as its center of mass is over the table.
Stable, Unstable and Neutral Equilibrium
To show that a double cone appears to roll uphill as its center of mass drops.
To show that a low center of gravity helps an object maintain a stable equilibrium.
To show that a low center of gravity helps a tightrope walker balance.
To show that a counterweight allows a tilted board to balance in stable equilibrium.
Resolution of Forces
1J30.10 Suspended Block on Incline
To resolve the forces acting on a block on an inclined plane.
To show how the mass of a cart affects the force it experiences.
To resolve the tension on a string into two components.
To show a hinged board can be used to break a string with only a small applied force.
Static Torque
To demonstrate that the magnitude of the normal force depends on the angle of the surface.
To demonstrate that torque is proportional to radius.
To show the relationship between torque, force, and radius.
To show increasing torque on a ladder eventually causes the ladder to sip.
Applications of Newton's Laws
Dynamic Torque
To show that the end of a board rotating under the force of gravity falls faster than g.
To show how torque can be used to lift a bucket.
To show the direction of rotation depends on the angle of the torque applied.
To demonstrate that a net torque causes an object to roll uphill.
Friction
1K20.10 Incline Plane and Block
To demonstrate the effects of different coefficients of friction.
To show friction acts against inertia.
1K20.30 Static and Dynamic Friction
To demonstrate static and dynamic friction.
To show that friction increases exponentially with area.
Pressure
To show the strength of the frictional force between the pages of two books.
To illustrate the relationship between force and pressure.
Gravity
Universal Gravitational Constant
Orbits
To measure the gravitational constant.
1L10.20 Model Cavendish Balance
To model the Cavendish experiment.
To illustrate orbital motion in a gravitational potential well.
1L20.17 Ball Rolling in a Funnel
To show how a ball’s orbit changes as it rolls down a funnel.
To demonstrate different possible orbital paths.
To draw an ellipse from two foci.
Work and Energy
Work
Simple Machines
Non-Conservative Forces
To show the equivalence of energy and work.
To demonstrate the mechanical advantage of different pulley configurations.
To demonstrate the mechanical advantage of different classes of lever arms.
1M30.10 Sliding Mass on a Glider
To demonstrate the energy lost in an inelastic collision.
Conservation of Energy
To show conservative and nonconservative changes in mechanical energy.
1M40.10 Bowling Ball Nose Basher
To demonstrate conservation of energy of a large pendulum.
1M40.15 Galileo's Stopped Pendulum
To show that the energy of a pendulum is conserved throughout its swing even when its length is changed.
To illustrate the conversion of potential energy to translational and rotational kinetic energy.
1M40.25 Double Dip Energy Path
To demonstrate an energy barrier.
1M40.33 Triple Track Conservation of Energy
To show that three balls with the same initial potential energy which travel down different paths have the same final kinetic energy.
To show conservation of momentum in an inelastic collision.
To show conservation of energy as a ball rolls down an incline.
1M40.63 Two Carts and a Spring
To show how potential energy is converted to kinetic energy as two carts oscillate on a spring.
To show that the potential energy in a compressed spring is converted to kinetic energy when the spring is released.
To show the potential energy in a compressed spring is converted to the kinetic energy when the spring is released.
1M40.77 Energy Conservation of Simple Harmonic Motion
To calculate the kinetic, potential, and total energy of a cart oscillating between two springs.
1M40.78 Conservation of Energy Cart on an Incline
To show the kinetic, potential, and total energy of a cart on an incline.
Linear Momentum and Collisions
Impulse and Thrust
Conservation of Linear Momentum
To demonstrate impulse by catching a raw egg in a sheet without breaking it.
1N20.10 Constant Velocity Air Track
To demonstrate conservation of linear momentum in the absence of friction.
1N20.13 Two Carts and a Spring
To show that when a spring between two carts is compressed and released, the carts move apart with equal and opposite momentum.
Rockets
Collisions in One Dimension
1N20.18 Metronomes on a Rolling Board
To show that metronomes on a rolling board become synchronized after a few cycles due to conservation of momentum.
To demonstrate conservation of momentum propels a rocket car forward.
To show the force of air shooting out of a balloon propels the balloon forward.
To demonstrate conservation of momentum and energy in elastic collisions.
Collisions in Two Dimensions
1N30.30 Elastic & Inelastic Collisions Dynamic Track
To illustrate elastic and inelastic collisions.
1N30.33 Elastic Collisions Air Track
To show conservation of energy and momentum during elastic collisions of objects with different masses and velocities in the absence of friction.
1N30.60 Basketball and Tennis Ball
To show the transfer of momentum in a collision between two balls with very different masses.
To demonstrate elastic collisions in two dimensions.
To demonstrate scattering of two balls at different gravitational potentials.
Rotational Dynamics
Moment of Inertia
1Q10.10 Moment of Inertia Bars
To show two bars with the same length and mass have different moments of inertia.
To show the moment of inertia of a torsion pendulum is directly proportional to its period of oscillation.
1Q10.40 Moment of Inertia Race
To show an object’s angular acceleration depends on its moment of inertia.
1Q10.41 Rotation & Adjustable Moment of Inertia
To show the angular velocity of a spinning object depends on its moment of inertia.
Rotational Energy
To show that moment of inertia is resistance to angular acceleration.
1Q10.80 Parallel Axis Theorem Disk
To demonstrate the parallel axis theorem.
To show the energy of a falling mass is converted into rotational energy of a spinning object.
To demonstrate the conversion of rotational kinetic energy into translational kinetic energy.
Transfer of Angular Momentum
Conservation of Angular Momentum
To demonstrate the conversion of potential energy into rotational and translational kinetic energy.
To show linear momentum is converted to angular momentum when a projectile lands on the rim of a bicycle wheel.
To show that an object rotates about an axis when struck at the corresponding center of percussion.
1Q40.10 Rotating Stool and weights
To demonstrate conservation of angular momentum.
To demonstrate that angular momentum is conserved as the moment of inertia and angular velocity of a cork on a string changes.
To demonstrate that angular momentum is conserved as the moment of inertia of a rotating sphere changes.
To show angular momentum is conserved when a ball's radius of orbit is increased and decreased.
1Q40.30 Spinning Wheel and Stool
To show angular momentum is conserved when a torque is applied to a spinning wheel.
To show the conversion of translational momentum to angular momentum.
1Q40.56 Acrobatic Astronauts (Video)
To show the conservation of angular momentum in the absence of gravity.
1Q40.63 Unbalanced Flywheel on a Stick
To demonstrate the conservation of angular momentum in an unbalanced flywheel.
To show an unbalanced wheel wobbles as it spins to conserve angular momentum.
Gyros
1Q40.70 Ball Rolling in a Funnel
To show that a ball rolling down a funnel conserves angular momentum.
To show the conversion of linear to angular momentum in a glass boiler.
To show the precession of a gyroscope on a pedestal.
1Q50.10 Counterbalanced Gyroscope
To show the precession and nutation of a counterbalanced gyroscope.
Rotational Stability
To show precession with a bicycle wheel.
To show the response of a gyroscope to an applied force.
To demonstrate the precession and nutation of a gyroscope without friction.
To illustrate stable rotation at high angular velocities.
To demonstrate unstable rotation.
To show unusual rotational stability.
1Q60.40 Stable and Unstable Axes
To illustrate stable and unstable axes of rotation.
Properties of Matter
Hooke's Law
Tensile and Compressive Stress
To show the distance a spring stretches is proportional to the force applied.
1R10.11 Series & Parallel Springs
To demonstrate effective spring constants of springs in series and parallel.
1R20.01 Compression of a Spring
To introduce the concept of compression.
To demonstrate Young's modulus.
Shear Stress
Coefficient of Restitution
To demonstrate the different strains felt by the different portions of a bent beam.
To show the stress and strain within a material using polarized light.
To demonstrate the effects of shear stress and strain.
To demonstrate the effect of a material’s coefficient of restitution.