# A solid disk, spinning counter-clockwise, has a mass of 7 kg and a radius of 8/3 m. If a point on the edge of the disk is moving at 1/4 m/s in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

Jun 13, 2017

The angular momentum is $= 2.33 k g {m}^{2} {s}^{-} 1$ and the angular velocity is $= 0.09375 r a {\mathrm{ds}}^{-} 1$

#### Explanation:

The angular velocity is

$\omega = \frac{\Delta \theta}{\Delta t}$

$v = r \cdot \left(\frac{\Delta \theta}{\Delta t}\right) = r \omega$

$\omega = \frac{v}{r}$

where,

$v = \frac{1}{4} m {s}^{- 1}$

$r = \frac{8}{3} m$

So,

$\omega = \frac{\frac{1}{4}}{\frac{8}{3}} = \frac{3}{32} = 0.09375 r a {\mathrm{ds}}^{-} 1$

The angular momentum is $L = I \omega$

where $I$ is the moment of inertia

For a solid disc, $I = \frac{m {r}^{2}}{2}$

So, $I = 7 \cdot {\left(\frac{8}{3}\right)}^{2} / 2 = \frac{224}{9} k g {m}^{2}$

The angular momentum is

$L = \frac{224}{9} \cdot \frac{3}{32} = \frac{7}{3} = 2.33 k g {m}^{2} {s}^{-} 1$