9% of the Physics C test is based on rotation including the following topics:
Successful students will be able to:
• Understand simple harmonic motion, so they can:
o Sketch or identify a graph of displacement as a function of time, and determine from such a graph the amplitude, period, and frequency of the motion.
o Write down an appropriate expression for displacement of the form Atsinw or Atcosw to describe the motion.
o Find an expression for velocity as a function of time.
o State the relations between acceleration, velocity, and displacement, and identify points in the motion where these quantities are zero or achieve their greatest positive and negative values.
o State and apply the relation between frequency and period.
o Recognize that a system that obeys a differential equation of the form 222dxdtxw=- must execute simple harmonic motion, and determine the frequency and period of such motion.
o State how the total energy of an oscillating system depends on the amplitude of the motion, sketch or identify a graph of kinetic or potential energy as a function of time, and identify points in the motion where this energy is all potential or all kinetic.
o Calculate the kinetic and potential energies of an oscillating system as functions of time, sketch or identify graphs of these functions, and prove that the sum of kinetic and potential energy is constant.
o Calculate the maximum displacement or velocity of a particle that moves in simple harmonic motion with specified initial position and velocity.
o Develop a qualitative understanding of resonance so they can identify situations in which a system will resonate in response to a sinusoidal external force.
• Apply their knowledge of simple harmonic motion to the case of a mass on a spring, so they can:
o Derive the expression for the period of oscillation of a mass on a spring.
o Apply the expression for the period of oscillation of a mass on a spring.
o Analyze problems in which a mass hangs from a spring and oscillates vertically.
o Analyze problems in which a mass attached to a spring oscillates horizontally.
o Determine the period of oscillation for systems involving series or parallel combinations of identical springs, or springs of differing lengths.
• Apply their knowledge of simple harmonic motion to the case of a pendulum, so they can:
o Derive the expression for the period of a simple pendulum.
o Apply the expression for the period of a simple pendulum.
o State what approximation must be made in deriving the period
o Analyze the motion of a torsional pendulum or physical pendulum in order to determine the period of small oscillations.
• Know Newton’s Law of Universal Gravitation, so they can:
o Determine the force that one spherically symmetrical mass exerts on another.
o Determine the strength of the gravitational field at a specified point outside a spherically symmetrical mass.
o Describe the gravitational force inside and outside a uniform sphere, and calculate how the field at the surface depends on the radius and density of the sphere.
• Understand the motion of an object in orbit under the influence of gravitational forces, so they can:
o For a circular orbit:
. Recognize that the motion does not depend on the object’s mass; describe qualitatively how the velocity, period of revolution, and centripetal acceleration depend upon the radius of the orbit; and derive expressions for the velocity and period of revolution in such an orbit.
. Derive Kepler’s Third Law for the case of circular orbits.
. Derive and apply the relations among kinetic energy, potential energy, and total energy for such an orbit.
o For a general orbit:
. State Kepler’s three laws of planetary motion and use them to describe in qualitative terms the motion of an object in an elliptical orbit.
. Apply conservation of angular momentum to determine the velocity and radial distance at any point in the orbit.
. Apply angular momentum conservation and energy conservation to relate the speeds of an object at the two extremes of an elliptical orbit.
. Apply energy conservation in analyzing the motion of an object that is projected straight up from a planet’s surface or that is projected directly toward the planet from far above the surface.
Week 8: Read/Scan/Use: HR&W Chapter 13 & 15
Do: Chapter 13:
Chapter 15: