Energy and Momentum of Rotating Systems

Six topics carry rotational ideas into energy and momentum, then out to orbit. Rotational kinetic energy is the energy stored in spin. Torque and work connects a torque acting through an angle to the energy it delivers. Angular momentum and angular impulse are the rotational analogues of linear momentum and impulse. Conservation of angular momentum governs any system with no net external torque, from a spinning skater pulling her arms in to a collapsing star. Rolling combines translation and rotation under the no-slip constraint. Motion of orbiting satellites applies energy and angular momentum conservation to bodies bound by gravity.

Topics

6.1

Rotational Kinetic Energy

Torque and Work

Angular Momentum and Angular Impulse

Conservation of Angular Momentum

Rolling

Motion of Orbiting Satellites

Lesson

Diagnostic

after diagnostic

Equations From the AP Physics 1 equation sheet

Rotational kinetic energy

$K = \tfrac{1}{2} I \omega^2$

Work by a torque

$W = \tau \, \Delta\theta$

Rolling, speed link

$v = r \omega$

Rolling, displacement link

$\Delta x_{\text{cm}} = r \, \Delta\theta$

Angular momentum (rigid body)

$L = I \omega$

Angular momentum (particle)

$L = r m v \sin\theta$

Angular impulse

$\Delta L = \tau \, \Delta t$

Newton's law of gravitation

$F_g = G \dfrac{m_1 m_2}{r^2}$

Gravitational potential energy

$U_G = - \dfrac{G m_1 m_2}{r}$

Centripetal acceleration

$a_c = \dfrac{v^2}{r}$

Unit 6 tools

Challenge bank

1 / 60

60 open-ended problems.

Read the question, work it out, then flip the card to compare your reasoning to the worked solution. Mark each card so you can return to the ones that still bite.

Question

Tap card to reveal explanation

Worked solution

Tap card to return to question

Cumulative assessment

Test the unit.

Twenty mixed items pulled from across all 6 topics. Identifies which misconceptions still bite when you cannot see which topic the question came from.

Begin assessment →

Check what stuck.

Units 1 through 6, drawn evenly so earlier units get the same share as this one. Twenty questions or a full 42-question section, your choice. Even coverage means this is a retention check rather than a score estimate.

Begin assessment →

Rolling race lab

Collect your own data, choose the transform that straightens the plot, and read a shape factor off the slope. Results record to your class dashboard.

Open the lab →