# A solid disk, spinning counter-clockwise, has a mass of 4 kg and a radius of 3/7 m. If a point on the edge of the disk is moving at 5/2 m/s in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

Aug 9, 2017

The angular momentum is $= 2.14 k g {m}^{2} {s}^{-} 1$ and the angular velocity is $= 5.83 r a {\mathrm{ds}}^{-} 1$

#### Explanation:

The angular velocity is

$\omega = \frac{\Delta \theta}{\Delta t}$

$v = r \cdot \left(\frac{\Delta \theta}{\Delta t}\right) = r \omega$

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

where,

$v = \frac{5}{2} m {s}^{- 1}$

$r = \frac{3}{7} m$

So,

$\omega = \frac{\frac{5}{2}}{\frac{3}{7}} = \frac{35}{6} = 5.83 r a {\mathrm{ds}}^{-} 1$

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, $I = 4 \cdot {\left(\frac{3}{7}\right)}^{2} / 2 = \frac{18}{49} k g {m}^{2}$

The angular momentum is

$L = \frac{18}{49} \cdot \frac{35}{6} = 2.14 k g {m}^{2} {s}^{-} 1$