AP® Physics 1: Algebra-Based review sheet from Aim for Five (aimforfive.com/physics/units/6)
Unit 6
5–8% of examEnergy and Momentum of Rotating Systems
This unit brings energy and momentum, two of physics' most useful ideas, to spinning objects. You'll find rotational kinetic energy, see how torques do work, use angular momentum and angular impulse, explain why a skater spins faster when pulling in their arms, analyze objects rolling without slipping, and apply the conservation laws to satellites in orbit.
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Flashcards (29)Practice questions (55)Physics 1 must-know sheetFree-response questions on this unit
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- Translation between representations (TBR)Satellite orbits and escape12 points · about 28 minutes
- Translation between representations (TBR)Racing a sphere and a hoop down a ramp12 points · about 28 minutes
- Qualitative/quantitative translation (QQT)Dropping a disk onto a spinning disk8 points · about 18 minutes
Big ideas
- A spinning object has kinetic energy even if its center stays still: K = ½Iω²
- A torque acting through an angle does work: W = τΔθ
- Angular momentum stays constant when there is no net external torque
- A rolling object's kinetic energy is part translational and part rotational
- Orbits obey conservation of energy and angular momentum
Full unit reviews
Longer videos that cover the whole unit. Good for a first pass or a final review.
Topics
A spinning object has rotational kinetic energy K = ½Iω², because every part of it is moving even when its center of mass stays put. If the object also moves as a whole, its total kinetic energy is the translational part (½Mv² for its center of mass) plus the rotational part, and like all energy it's a scalar.
Key terms
- rotational kinetic energy
- translational kinetic energy
- total kinetic energy
- scalar
A few quick questions on this topic, with the answers explained.
A torque that acts while an object turns through an angle transfers energy into or out of it; for a constant torque the work is W = τΔθ, with Δθ in radians. When the torque changes, the work is the area under a graph of torque versus angular position.
Key terms
- work done by a torque
- angular displacement
- torque versus angle graph
- energy transfer
- rotational kinetic energy
A few quick questions on this topic, with the answers explained.
A rotating rigid object has angular momentum L = Iω, and even an object moving in a straight line has angular momentum about a point, L = rmv sin θ, which depends on the point you choose. Angular impulse is torque multiplied by the time it acts (the area under a torque–time graph), and it equals the change in angular momentum.
Key terms
- angular momentum
- angular momentum of a point object
- angular impulse
- torque–time graph
- angular impulse–momentum theorem
A few quick questions on this topic, with the answers explained.
If no net external torque acts on a system, its total angular momentum stays constant. That's why a skater who pulls in their arms (lowering their rotational inertia) spins faster, and why in a collision the angular momentum one object loses, another gains. A torque from outside the system changes the system's angular momentum.
Key terms
- conservation of angular momentum
- net external torque
- choosing a system
- rotational collision
- changing rotational inertia
A few quick questions on this topic, with the answers explained.
Rolling
When an object rolls without slipping, its center-of-mass motion and its spin are locked together (v = rω and a = rα), its kinetic energy is ½Mv² + ½Iω², and static friction removes no energy. When it slips, kinetic friction turns some energy into thermal energy and v and ω are no longer linked, and AP Physics 1 only asks you to describe that case in words.
Key terms
- rolling without slipping
- kinetic friction
- static friction
- translational and rotational kinetic energy
- slipping
A few quick questions on this topic, with the answers explained.
When a satellite orbits a much more massive object and only gravity acts, the total mechanical energy of the pair stays constant, and so does the satellite's angular momentum. Gravitational potential energy is U = −GMm/r (zero at infinite distance), so in an elliptical orbit the satellite speeds up as it gets closer, trading potential energy for kinetic. Escape velocity, v = √(2GM/r), is the speed at distance r that makes the total energy exactly zero.
Key terms
- gravitational potential energy
- circular orbit
- elliptical orbit
- escape velocity
- conservation of angular momentum
A few quick questions on this topic, with the answers explained.