Question

A homogeneous disc of mass 2kg and radius 15 cm rotating with angular velocity of 4 rad/s. The linear momentum?

Answer 1

The formula for angular momentum is:

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

For a disk,

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

For this disk,

$I=\frac{1}{2} MR^2=\frac{1}{2} (2)\times 0.15^2=0.0225kgm^2 \\L=Iw=0.0225kgm^2\times(4 rad/s)=0.09kgm^2rad/s.$

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,

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

Answer 2

Linear momentum of disc rotating about a fixed axis is zero