Question

A uniform sphere of radius r= 0.500m and mass m= 15.0kg turns counter clockwise about a vertical axis through its center. Find its vector angular momentum about this axis when its angular speed is 3.00rad/sec.

Answer 1

The magnitude of angular momentum is

$$L=I\omega=\frac{2}{5}mr^2\cdot\omega=4.5\text{ kg}\cdot\text{m}^2/\text{s}^2.$$

If we look at the ball so that it rotates counter-clockwise, the angular momentum is directed in positive z-direction (toward us, out of the screen):

$$\textbf{L}=4.5\hat{z} \text{ kg}\cdot\text{m}^2/\text{s}^2$$