Question

A homogeneous disc of mass 2 kg and radius 15 cm is rotating about its axis (which is fixed) with an angular velocity of 4 rad/s. The linear momentum of the disc is :

• A. 1.2 kg-m/s
• B. 1.0 kg-m/s
• C. 0.6 kg-m/s
• D. None of the above

Answer 1

The correct option is C 0.6 kg-m/s

The formula for angular momentum is:

$L=Iw$, where is the angular velocity and $I$ is the moment of inertia.

For a disk$,$

$I=\frac{1}{2}M{R}^2,$ where $M$ is the mass of the disk and $R$ is the radius of the disk.

For this disk,

$I=\frac{1}{2}M{R}^2=\frac{1}{2}\left(2\right)\times {\left(0.15\right)}^2=0.0225kg{m}^2$

$L=Iw=0.0225kg{m}^2\times \left(4rad/s\right)=0.09kg{m}^{2}rad/s$

The linear momentum is related to the the angular momentum by the formula; $L=pr.$

We can solve for p, the linear momentum in this equation to get,

$p=\frac{L}{r}=\frac{0.09}{0.15}=0.6kgs$

Hence,

option $\left(C\right)$ is correct answer.