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6.2.2Energy and Momentum of Rotating Systems

Angular Impulse — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 9 parts Lesson 5 of 13 1 quiz

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Lesson summary

6.2.2 Angular Impulse — AP PHYSICS 1 notes: Define angular impulse and use it to find the change in angular momentum produced by a torque acting over time.Angular impulse = the product of the average torque and the time interval over which it acts, τΔt.Unit — N·m·s = kg·m2/s, the…

  • Linear analogue
  • τΔt = ΔL = Lf − Li
  • Rigid body about a fixed axis
  • Generality
  • Convention
  • Torque along L

Section 1 of 9Definition

Angular impulse
Angular impulse the product of the average torque and the time interval over which it acts, τΔt.
Unit
  • N·m·s = kg·m2/s, the unit of angular momentum.
Direction
  • Direction same as the net torque; zero average torque gives no angular impulse.
Linear analogue
  • FΔt changes momentum, so τΔt changes angular momentum.

Section 2 of 9Link to angular momentum

Link to angular momentum
τΔt
ΔL = Lf − Li
  • from Στ = ΔL/Δt.
Rigid body about a fixed axis
  • ΣτΔt = I(ωf − ωi) = IΔω.
Generality
  • Generality also valid when I changes during the motion, unlike Στ = Iα used simply.

Section 3 of 9Sign and direction

Convention
  • Convention counterclockwise positive, clockwise negative.
Torque along L
  • Torque along L increases its magnitude.
Torque against L
  • Torque against L decreases it, and acting long enough it reverses the rotation.

Section 4 of 9Applying angular impulse

1
Find the torque from each force, τ = rF sinθ.
2
Multiply by the time for which it acts.
3
Set the result equal to the change in angular momentum.
4
Divide by I to find the change in angular velocity.
Best for
  • Best for short torques where time is known.
    • (a bat hitting a ball, a hammer striking a rod)
Variable torque
  • Variable torque use the average torque or the area under the torque–time graph.

Section 5 of 9Comparison with linear motion

LinearAngular
Force FTorque τ
Momentum pAngular momentum L
Mass mRotational inertia I
Impulse FΔt = ΔpAngular impulse τΔt = ΔL
  • Same impulse, different I
    • same ΔL but different Δω because ω = L/I; a larger I gives less change in spin rate.

Section 6 of 9Impulse versus work

QuantityInvolvesChanges
Angular impulse τΔtTimeAngular momentum
Work τΔθAngleKinetic energy
1Starting from rest with constant τ
  • Starting from rest with constant τ impulse gives ω = τt/I;
    • work gives ½Iω2 = τΔθ with Δθ = ½(τ/I)t2;
    • both agree.
2Choose impulse
  • Choose impulse for short interactions with known duration.
3Choose work
  • Choose work when the angle or number of turns is known.
4Unit check
  • N·m·s divided by kg·m2 leaves s−1.

Section 7 of 9More from the specification

More from the specification
Distance
  • Total length of path travelled, a scalar.
Collision
  • Short interaction with large internal forces.
Newton
  • Unit of force, kg m s-2.
External torque
  • Torque produced by a force from outside the system.
Rigid system
  • System that holds its shape while rotating.

Section 8 of 9Key terms

TermMeaning
Angular impulseProduct of net torque and the time it acts, τΔt.
TorqueRotational effect of a force, τ = rF sinθ.
Change in angular momentumΔL = Lf − Li, equal to the angular impulse.
Net torqueSum of all external torques on the system.
N·m·sUnit of angular impulse.

Section 9 of 9Exam technique

1
Confusing angular impulse τΔt with linear impulse FΔt.
2
Forgetting to use the net torque when several torques act.
3
Using angular impulse where the angle is given but not the time.
4
Dropping the sign when a torque opposes the rotation.
5
Calculating Δω as impulse times I instead of impulse divided by I.

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