Question

A uniform disk of mass 3.25 kg has a radius of 0.100 m and spins with a frequency of 0.550 rev/s. What is its angular momentum?

Answer 1

ANSWER:

0.0562 J

STEP-BY-STEP EXPLANATION:

Angular momentum is expressed in terms of moment of inertia and angular velocity. This is expressed as follows:

$L=I\cdot\omega$

Here, I is the angular momentum and ω is the angular velocity.

Angular momentum is mass time the square of the radius of the object. Moment of inertia for a uniform disk is given as,

$I=\frac{1}{2}m\cdot r^2$

Here, m is the mass of the disk and r is the radius of the disk.

Replacing:

$L=\frac{1}{2}m\cdot r^2\cdot\omega$

Convert the units of angular velocity into rad/s.

$\begin{gathered} \omega=0.55\text{ rev/s}\cdot\frac{2\pi\text{ rad}}{1\text{ rev}} \\ \omega=3.46\text{ rad/s} \end{gathered}$

We replace each data to calculate the angular momentum:

$\begin{gathered} L=\frac{1}{2}\cdot3.25\cdot0.1^2\cdot3.46 \\ L=0.0562 \end{gathered}$

The angular momentum of the uniform disk is 0.0562 J