Energy and Momentum of Rotating Systems

What the exam asks

• Split the kinetic energy of rolling objects into translational and rotational parts
• Race rolling shapes down inclines using energy partition arguments
• Apply the rolling constraint linking v and ω
• Compute angular momentum for spinning objects and moving point masses
• Use conservation of angular momentum when net external torque is zero (skaters, rotational collisions)

Key formulas and rules

Question bank breakdown

Skills covered

Every question in the bank comes with a worked explanation, and most add a per-choice breakdown so you learn why each wrong answer is wrong - not just the key.

Sample question

From the free tier of the ScoreMint AP Physics 1 bank - try it, then check the answer.

A thin hoop and a solid disk have the same mass $M$ and the same radius $R$. Both start from rest at the top of an inclined plane and roll without slipping to the bottom. Which object reaches the bottom first, and why?

• A. The hoop reaches the bottom first because it has a larger rotational inertia and therefore more angular momentum.
• B. The solid disk reaches the bottom first because a smaller fraction of its kinetic energy is rotational.
• C. They reach the bottom at the same time because they have the same mass and radius.
• D. The hoop reaches the bottom first because circular shapes roll more efficiently.

Study tip

When a mass sticks to a rotating rod or disk, conserve angular momentum, never linear momentum or energy - the axle supplies external forces but no torque about itself.