# A solid disk, spinning counter-clockwise, has a mass of 14 kg and a radius of 5/4 m. If a point on the edge of the disk is moving at 7/9 m/s in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

Dec 12, 2016

The angular momentum is $= 170.6 k g {m}^{2} {s}^{- 1}$
The angular velocity is $= 3.9 r a {\mathrm{ds}}^{- 1}$

#### Explanation:

The angular velocity is $\omega$

$\omega = \frac{v}{r} = \frac{7}{9} \cdot \frac{4}{5} \cdot 2 \pi r a {\mathrm{ds}}^{- 1}$

$= \left(\frac{56}{45} \pi\right) r a {\mathrm{ds}}^{- 1} = 3.9 r a {\mathrm{ds}}^{- 1}$

The angular momentum is $L = I \omega$

For a solid disc, the moment of inertia $I = \frac{1}{2} m {r}^{2}$

$I = \frac{1}{2} \cdot 14 \cdot \frac{25}{4} = \frac{175}{4} k g {m}^{2}$

The angular momentum is

$L = \frac{175}{4} \cdot \frac{56}{45} \cdot \pi = 170.6 k g {m}^{2} {s}^{- 1}$