Angular Momentum
- Compute angular momentum as L = Iω
- Find the angular momentum of a point mass moving in a circle, L = mvr
- Treat angular momentum as a vector along the rotation axis
Angular momentum: rotational momentum
Angular momentum L is the rotational counterpart of linear momentum. For an extended rotating body it is L = Iω — rotational inertia times angular velocity — measured in kg·m²/s. Just as linear momentum measures how hard it is to stop a moving object, angular momentum measures how hard it is to stop a spinning one. A massive, fast-spinning flywheel has enormous angular momentum.
A single particle in a circle
For a point mass moving in a circle of radius r at speed v, the angular momentum about the center is L = mvr. This is just L = Iω with I = mr² and v = rω. It shows that angular momentum depends not only on how fast and how heavy, but on how far from the axis — the same mass and speed farther out carries more angular momentum.
A disk with rotational inertia 3 kg·m² spins at 4 rad/s. Find its angular momentum.
- 1.Use L = Iω.
- 2.Substitute the values: L = 3 × 4.
- 3.Compute: L = 12 kg·m²/s.
- 4.The vector points along the axis, in the direction the right hand’s fingers curl with the spin.
The two formulas are the same idea: L = Iω for a whole body, L = mvr for a single orbiting particle. If you are given v and r, use mvr; if given I and ω, use Iω.
A disk with rotational inertia 2 kg·m² rotates at 6 rad/s. What is its angular momentum?
A 0.5 kg ball moves at 4 m/s in a circle of radius 2 m. What is its angular momentum about the center?
Angular momentum is a vector along the rotation axis. On the AP exam its direction matters most in conservation problems, where the total vector — magnitude and direction — must stay constant.
Answer the 2 checkpoints as you read.
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