A solid disk, spinning counter-clockwise, has a mass of 15 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?

Jan 22, 2017

The angular momentum is $= 1320 k g m {s}^{- 1}$
The angular velocity is $= 11 r a {\mathrm{ds}}^{-} 1$

Explanation:

The angular velocity is

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

where,

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

$r = 4 m$

So,

$\omega = \frac{7}{4} \cdot 2 \pi = \frac{7}{2} \pi = 11 r a {\mathrm{ds}}^{-} 1$

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, $I = 15 \cdot {\left(4\right)}^{2} / 2 = 120 k g {m}^{2}$

$L = 11 \cdot 120 = 1320 k g m {s}^{- 1}$