# A solid disk, spinning counter-clockwise, has a mass of 2 kg and a radius of 7/2 m. If a point on the edge of the disk is moving at 15/4 m/s in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

Nov 10, 2016

The angular velocity is $= \frac{15}{14} H z$
The angular momentum $= \frac{105}{4} k g {m}^{2} {s}^{-} 1$

#### Explanation:

The angular velocity $\omega = \frac{v}{r}$
$v =$ velocity $= \frac{15}{4} m {s}^{- 1}$
and $r =$ radius $= \frac{7}{2} m$
So $\omega = \frac{15}{4} \cdot \frac{2}{7} = \frac{15}{14} H z$

The angular momentum is $L = I . \omega$
$I =$ moment of inertia $= m {r}^{2} / 2$
$I = 2 \cdot {\left(\frac{7}{2}\right)}^{2} = 2 \cdot \frac{49}{4} = \frac{49}{2} k g {m}^{2}$
$L = \frac{49}{2} \cdot \frac{15}{14} = \frac{105}{4} k g {m}^{2} {s}^{- 1}$