6.4 Transfer of Angular Momentum

In Unit 4, we learned about how linear momentum can be transferred through exerting a force over a period of time. Using a similar idea, angular momentum can be transferred through exerting a torque on a rigid body over a period of time, which is known as the angular impulse. This angular impulse will result in a change in angular momentum for the rigid body in the direction that the angular impulse was applied in. A body's angular momentum will change in the direction of the torque exerted on the body.

This equation can actually be used to derive Newton’s 2nd Law in Rotational Form. By solving for torque, you get ${\tau=\frac{\Delta L}{\Delta t}}$. Assuming the rotational inertia of a rigid body stays constant, we can get ${\Delta L=I \Delta \omega}$, which gets us the equation ${\tau =I \frac{\omega}{\Delta t}}$. Since ${\alpha=\frac{\Delta \omega}{\Delta t}}$, we can plug that in, getting the final equation of ${\tau=I \alpha}$.

The change in angular momentum of a rigid body is just a body's final angular momentum minus its initial angular momentum.

-${\Delta L}$ represents the change in angular momentum of a rigid body