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Theme A — Space, Time and Motion

A.4.7 Angular Momentum — IB Physics HL Revision Notes & Topical Questions

5 min read 8 parts Lesson 49 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision
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pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
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Lesson summary

A.4.7 Angular Momentum — IB PHYSICS HL notes: Define angular momentum, calculate it for point masses and apply its conservation.Angular momentum is the rotational equivalent of linear momentum p = mv.L = IωL is in kg m2 s-1, I is moment of inertia and ω is angular velocity.It is …

  • It is a vector along the axis
  • A point mass has I
  • Just before a particle M at speed v hits a container at distance R, L
  • A decrease in I means an increase in ω
  • It follows from τ
  • A diver tucks in limbs during a jump

Part 1 of 6Definition

Definition
Angular momentum is the rotational equivalent of linear momentum p
Angular momentum is the rotational equivalent of linear momentum p mv.
L
Iω
  • L is in kg m2 s-1, I is moment of inertia and ω is angular velocity.
It is a vector along the axis
  • It is a vector along the axis for planar problems clockwise or anticlockwise sign is enough.

Part 2 of 6Angular momentum of a point mass

Angular momentum of a point mass
A point mass has I
A point mass has I mr2 and ω = v/r.
So L
Iω = (mr2)(v/r) = mvr.
A particle moving in a straight line has angular momentum about any axis it does not pass through.
  • It depends on the position of the object relative to the axis chosen.
Just before a particle M at speed v hits a container at distance R, L
MvR.
  • After sticking, with a system of M and 3M at distance R, L = 4MR2ω.

Part 3 of 6Conservation of angular momentum

1
Total angular momentum of a system stays constant unless a net resultant torque acts.
2Iiωi
Ifωf for constant total angular momentum.
3A decrease in I means an increase in ω
  • A decrease in I means an increase in ω and the reverse.
4It follows from τ
ΔL/Δt — zero torque gives zero change.

Part 4 of 6Applications

1
A person on a spinning chair spins faster with arms and legs pulled in.
2
Ice skaters extend or pull in the arms to change their rotation speed.
3A diver tucks in limbs during a jump
  • I decreases and ω increases.
4
Objects in elliptical orbits move faster nearer the body they orbit.
5
Tornados spin faster as their radius decreases.
6After leaving the springboard no torque acts
  • After leaving the springboard no torque acts so angular momentum is constant.

Part 5 of 6Method for problems

Method for problems
Identify the system and check no external torque acts.
Write Linitial and Lfinal using L = Iω or L = mvr.
Equate them and solve for the unknown ω or I.
Method for problems
Include every part of the system in the moment of inertia, e.g. a body that gains or loses mass.
Add moments of inertia about the same axis only.

Part 6 of 6More from the specification

More from the specification
Conservation of angular momentum
  • Conservation of angular momentum when no external resultant torque acts on a rotating system, total angular momentum remains strictly constant over time.
Rotational kinetic energy of flywheels
  • Rotational kinetic energy of flywheels rotating bodies store rotational kinetic energy proportional to their moment of inertia and angular velocity squared, E = ½Iω².
Rotational equilibrium under opposing couples
  • Rotational equilibrium under opposing couples an extended rigid body remains in rotational equilibrium when opposing couple forces exert zero net turning moment.
Angular momentum definition
  • For a particle moving in a circle, angular momentum is L = m * v * r = I * omega,
  • where I is moment of inertia and omega is angular velocity.
Conservation of angular momentum
  • When net external torque acting on a rotating system is zero (Sigma tau = 0), total angular momentum remains strictly conserved.
Rotational dynamics and torque
  • Torque is the rotational analogue of force, governing angular acceleration in rigid rotating bodies.
    • (tau = I * alpha)
Kinetic energy
  • K = ½mv2, energy of motion.
Acceleration
  • Rate of change of velocity.
Force
  • A push or pull measured in newtons.
Displacement
  • Change in position.
Couple
  • A pair of equal opposite forces with different lines of action.
Equilibrium
  • State with zero net force.
Newton
  • Unit of force, kg m s-2.
Perpendicular
  • At right angles.
Impulse
  • J = FΔt = Δp.
    What the symbols mean: F = force (N) · Δt = time the force acts (s) · Δp = change in momentum (kg m s−1); FΔt is the impulse (N s)

Key terms

TermMeaning
Angular momentumL = Iω, rotational equivalent of linear momentum.
Conservation of angular momentumL is constant when no net torque acts.
Moment of inertiaResistance to change in rotational motion.
Angular velocityRate of change of angular displacement.
Net torqueResultant torque on a body.
Point massMass at a single point, L = mvr.

Avoid these mistakes

1
Saying only rotating objects have angular momentum — a straight-moving mass has it about an axis.
2
Forgetting to include all masses in I after a collision.
3
Using linear momentum conservation when a torque acts through an axis.
4
Thinking angular velocity must stay constant when angular momentum is conserved.
5
Forgetting that L depends on the axis chosen.

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