Energy & Momentum of Rotating Systems

AP Physics 1 • Unit 85-8%

Applying energy and momentum concepts to rotating objects. Understand rotational kinetic energy, angular momentum, and powerful conservation laws.

Core Concepts

Rotational kinetic energy – KE = ½Iω² with work analysis
Angular momentum of rigid systems – L = Iω and particle angular momentum
Angular impulse – change in angular momentum, impulse-momentum theorem
Total mechanical energy – translational + rotational
Conservation of angular momentum – spinning systems with momentum changes
Orbital vs spin angular momentum – two types that add

Key Equations

$KE_{rot} = \frac{1}{2}I\omega^2$

$L = I\omega$

$\tau\Delta t = \Delta L$

$KE_{total} = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2$

$W = \tau\theta$

Real-World Applications

→Figure skating pirouettes – changing moment of inertia
→Rolling races – which shapes roll fastest?
→Rolling energy and slipping analysis
→Collisions with rotation and coaxial collisions

Topic Map

🎯Where This Unit Leads

Master this material to build a strong foundation for these career paths.

Mechanical Engineering

Flywheel design and rotating machinery

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Aerospace Engineering

Spacecraft attitude dynamics and control

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Physics

Angular momentum conservation in advanced mechanics

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