Question

Calculate the angular momentum of the following systems. Refer to Worksheet 19 for the

moment of inertia of highly-symmetric objects. For all items, you need to convert from

rpm to rad/s first.

Bicycle wheel with mass 2.0 kg and diameter 0.63 m rotating at a rate of 2.00

rpm. Assume that the bicycle wheel is a thin-walled hollow cylinder.

Answer 1

The moment of inertia of the thin-walled hollow cylinder:

$$I = mr^2$$

where $m = 2kg$ is the mass, and $r = 0.63m/2 = 0.315m$ is the radius of the wheel.

$$I = 2\cdot (0.315)^2 =0.19845 \space kg\cdot m^2$$

The angular frequency:

$$\omega = 2\pi\dfrac{2}{60} \approx 0.21\space rad/s$$

The angular momentum:

$$L = I\omega\\ L \approx 0.042\space kg\cdot m^2/s$$

Answer. 0.042 kg*m^2/s.