Angular Momentum of a Rigid Body

A spinning bicycle wheel resists being tilted because tilting it means changing the direction of its angular momentum vector, and that takes torque. The faster it spins or the more mass it has far from the axle, the bigger L is, and the harder you have to push to change it. This is the same stubbornness linear momentum shows against being changed, just rotated into the angular world.

Linear momentum packages an object's mass and velocity into one vector, p = mv. Angular momentum does the same job for rotation: L = I omega. Moment of inertia I plays the role of mass, telling you how the body's mass is spread relative to the axis, and angular velocity omega plays the role of velocity. Multiply them and you get a vector pointing along the rotation axis, by the right hand rule, whose size tells you how much rotational motion is locked up in the object. A single point mass moving in a circle is a special case: since its velocity is always perpendicular to the radius, L = I omega simplifies to L = mvr.

This setup matters most once you ask what makes L change. Just as net force changes p, net torque changes L, and when net external torque is zero, L is conserved. That conservation law is the real payoff of this topic, and it is what lets you solve problems like a skater pulling in her arms or two objects colliding and sticking while spinning. Rolling motion later in this unit uses L = I omega about the contact point to connect rotation and translation in one equation.