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

Dec 18, 2016

The angular momentum is $L = \left(140 \pi\right) k g {m}^{2} {s}^{- 1}$
The angular velocity is $\omega = \left(\frac{7}{2} \pi\right) r a {\mathrm{ds}}^{- 1}$

#### Explanation:

The angular velocity is $\omega = \frac{v}{r}$

$v = 7 m {s}^{- 1}$

$r = 4 m$

So,

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

The angular momentum is $L = I \omega$

Where,

$I =$ moment of inertia

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

$I = \frac{1}{2} \cdot 5 \cdot 4 \cdot 4 = 40 k g {m}^{2}$

The angular momentum is

$L = I \omega = 40 \cdot \frac{7}{2} \pi k g {m}^{2} {s}^{- 1}$

$L = 140 \pi k g {m}^{2} {s}^{- 1}$