← Physics C: Mechanics syllabus

United StatesPhysics C: Mechanics

Unit 6: Energy and Momentum of Rotating Systems

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

What is angular momentum, and how does an angular impulse from a torque change it, both for rigid bodies and for particles moving in a straight line?

Topic 6.3 Angular Momentum and Angular Impulse: define angular momentum for rigid bodies and particles, relate net torque to its rate of change, and use the angular impulse-momentum theorem.
A focused answer to AP Physics C: Mechanics Topic 6.3, covering angular momentum as $I\omega$ for rigid bodies and $\vec{r}\times\vec{p}$ for particles, the relation of net torque to the rate of change of angular momentum, and the angular impulse-momentum theorem, with worked examples.
11 min answer →

When is angular momentum conserved, and how do we use its conservation to analyze a spinning system whose rotational inertia changes or that is struck by a moving object?

Topic 6.4 Conservation of Angular Momentum: state that angular momentum is conserved when the net external torque is zero, and apply it to changing rotational inertia and rotational collisions.
A focused answer to AP Physics C: Mechanics Topic 6.4, covering the condition for angular momentum conservation (zero net external torque), the spinning-skater effect of changing rotational inertia, rotational collisions where a particle strikes a pivoted body, and why kinetic energy need not be conserved, with worked examples.
11 min answer →

How does gravity provide the centripetal force for orbits, and how do energy and angular momentum conservation describe circular and elliptical satellite motion?

Topic 6.6 Motion of Orbiting Satellites: derive the speed and period of a circular orbit, find the orbital energy, and apply conservation of energy and angular momentum to elliptical orbits and Kepler's laws.
A focused answer to AP Physics C: Mechanics Topic 6.6, covering gravity as the centripetal force for circular orbits, the orbital speed and period (Kepler's third law), the total orbital energy, escape speed, and conservation of energy and angular momentum in elliptical orbits, with calculus-aware worked examples.
11 min answer →

What is the rolling-without-slipping condition, and how do we combine it with energy and force methods to analyze rolling bodies?

Topic 6.5 Rolling: state the rolling-without-slipping constraints on velocity and acceleration, analyze the role of friction in rolling, and apply energy and dynamics methods to rolling bodies.
A focused answer to AP Physics C: Mechanics Topic 6.5, covering rolling without slipping and its velocity and acceleration constraints, the velocity distribution within a rolling body, the role of static friction, and analyzing a rolling body down an incline by energy and by force-torque methods, with worked examples.
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What is the kinetic energy of a rotating body, and how do translational and rotational kinetic energy combine for a body that both moves and spins?

Topic 6.1 Rotational Kinetic Energy: define rotational kinetic energy as $\tfrac{1}{2}I\omega^2$ , combine it with translational kinetic energy for a moving, spinning body, and use it in energy conservation.
A focused answer to AP Physics C: Mechanics Topic 6.1, covering rotational kinetic energy as half the rotational inertia times angular velocity squared, the total kinetic energy of a body that translates and rotates, and using rotational kinetic energy in energy conservation for rolling and falling spinning bodies, with worked examples.
10 min answer →

How does a torque do work as a body rotates, and how do the rotational work-energy theorem and rotational power parallel their translational forms?

Topic 6.2 Torque and Work: compute the work done by a torque as the integral of torque over angle, apply the rotational work-energy theorem, and define rotational power as $P = \tau\omega$ .
A focused answer to AP Physics C: Mechanics Topic 6.2, covering the work done by a torque as the integral of torque over angular displacement, the rotational work-energy theorem linking work to the change in rotational kinetic energy, and rotational power as torque times angular velocity, with calculus-based worked examples.
10 min answer →