Skip to content
Dabour HubLEARN · PRACTICE · EXPLORESign inStudent

6.3Energy and Momentum of Rotating Systems

Angular Momentum and Angular Impulse — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 9 parts Lesson 8 of 13 1 quiz

📚 AP PHYSICS 1 Hub / Topical Revision
🩺
100% Curriculum Specification Match Lesson Doctor Verified
The only platform with 100% curriculum specification match and verified interactive question banks.
0%read
Lesson summary

6.3 Angular Momentum and Angular Impulse — AP PHYSICS 1 notes: Describe the angular momentum of an object or rigid system and the angular impulse delivered to it.L = Iω — angular momentum about a specific axis, in kg·m2/s.Direction — clockwise or counterclockwise at AP level (rig…

  • Axis dependence
  • L = mvr sinθ
  • Straight-line motion
  • Line through the axis
  • Depends on
  • Torque–time graph

Section 1 of 9Angular momentum of a rigid system

Angular momentum of a rigid system
L = Iω
  • L = Iω angular momentum about a specific axis, in kg·m2/s.
Direction
  • Direction clockwise or counterclockwise at AP level.
    • (right-hand rule in general)
Axis dependence
  • Axis dependence always state the axis or reference point used.

Section 2 of 9Angular momentum of a particle

Angular momentum of a particle
L = mvr
  • L = mvr for a particle with the axis perpendicular to the plane of motion, from L = Iω = (mr2)(v/r).
L
L mvr sinθ
  • θ is the angle between r and v; L = mvr⊥.
Straight-line motion
  • Straight-line motion a particle on a line not through the reference point has angular momentum about it.
Line through the axis
  • Line through the axis gives zero angular momentum.
Depends on
  • Depends on distance from the reference point, mass, speed and the angle between r and v.

Section 3 of 9Angular impulse

Angular impulse
Angular impulse torque times the time over which it acts, τΔt, in N·m·s (= kg·m2/s).
Direction
  • Direction same as the torque.
Torque–time graph
  • Torque–time graph the area is the angular impulse.

Section 4 of 9Impulse–momentum theorem in rotational form

τnetΔt = ΔL
  • τnetΔt = ΔL net angular impulse equals the change in angular momentum.
Second law
  • τnet = ΔL/Δt; for constant I it reduces to τnet = Iα.
L–t graph
  • L–t graph its slope is the net external torque.
External torques only
  • External torques only internal torques cancel in pairs.

Section 5 of 9Linear versus angular

QuantityLinearAngular
Momentump = mvL = Iω
ImpulseFΔtτΔt
Graph areaF–t area = Δpτ–t area = ΔL
Point massNot applicablemvr (planet orbit)

Section 6 of 9Finding ΔL from a torque–time graph

1
Identify the axis and confirm the graph shows net external torque.
2
Split the area under the graph into rectangles and triangles.
3
Calculate each area, counting areas below the axis as negative.
4
Add the areas to get the net angular impulse = ΔL.
5
Use Lf = Li + ΔL, then ωf = Lf/I if needed.

Section 7 of 9More from the specification

Newton
  • Unit of force, kg m s-2.
Average torque
  • Constant torque giving the same angular impulse in the same time.
Velocity
  • Rate of change of displacement.
Inertia
  • Resistance of an object to changes in its motion.
Rotation
  • Motion in which an object turns about an axis.
Collision
  • Short interaction with large internal forces.

Section 8 of 9Key terms

TermMeaning
Angular momentumL = Iω for a rigid body; L = mvr⊥ for a particle.
Angular impulseτΔt = ΔL.
Torque–L linkΣτ = ΔL/Δt.
kg·m2/sUnit of angular momentum.
Reference pointPoint or axis about which L is measured.

Section 9 of 9Exam technique

1
Using different axes for L and I.
2
Forgetting L = mvr sinθ when the velocity is not perpendicular to r.
3
Counting internal torques in the net angular impulse.
4
Confusing angular impulse (N·m·s) with torque.

Last updated: