Angular Momentum
Rotational analog of linear momentum.
Formula
Variables
Example
Spinning skater conserves L
How it works
Angular momentum measures how hard it is to stop an object from rotating. For a rigid body spinning about a fixed axis, each bit of mass contributes more or less depending on how far it is from the axis, and that distribution is summarized by the moment of inertia I; multiplying by the angular speed \(\omega\) gives the total rotational momentum. This is the rotational counterpart to linear momentum \(p = mv\), and it is especially useful because angular momentum is conserved when the net external torque is zero.
When to use it
Use this formula when an object is rotating and you know its moment of inertia and angular velocity, or when you need to compare rotational motion before and after a change. It appears in problems involving spinning wheels, turntables, planets, machinery, and collisions or interactions where rotational motion matters.
Worked example, step by step
A solid disk has a moment of inertia of 2.5 kg·m^2 and spins at 12 rad/s. Step 1: Write the formula: L = I\omega Step 2: Substitute the values: L = (2.5 kg·m^2)(12 rad/s) Step 3: Multiply: L = 30 kg·m^2/s Final answer: The disk’s angular momentum is 30 kg·m^2/s.
Common mistakes to avoid
- Using rpm instead of rad/s without converting first
- Confusing moment of inertia with mass alone
- Forgetting that angular momentum depends on the chosen rotation axis
Did You Know?
A spinning skater speeds up by pulling in their arms — conservation of angular momentum in action.
Share this formula
More in Physics
View allNewton's Second Law
BasicForce equals mass times acceleration.
Kinetic Energy
BasicEnergy of a moving object.
Gravitational Potential Energy
BasicEnergy stored due to height in a gravitational field.
Work Done
BasicWork done by a force over a distance.
Power
BasicRate of doing work.
Momentum
BasicQuantity of motion of an object.