# A solid disk, spinning counter-clockwise, has a mass of 18 kg and a radius of 4 m. If a point on the edge of the disk is moving at 2/3 m/s in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

Nov 26, 2016

The angular momentum is $= 24 k g {m}^{2} {s}^{- 1}$
The angular velocity is $= \frac{1}{6} H z$

#### Explanation:

The angular velocity is $v = r \omega$

$v =$ velocity $= \frac{2}{3} m {s}^{- 1}$

and $r =$radius $= 4 m$

So, angular velocity, $\omega = \frac{v}{r} = \frac{2}{3} \cdot \frac{1}{4} = \frac{1}{6} H z$

The angular momentum is $L = I \cdot \omega$

where $I =$ moment of inertia

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

where $m =$ the mass $= 18 k g$

Therefore, $I = 18 \cdot 4 \cdot \frac{4}{2} = 144 k g {m}^{2}$

So, the angular momentum is $L = 144 \cdot \frac{1}{6} = 24 k g {m}^{2} {s}^{- 1}$