A solid disk, spinning counter-clockwise, has a mass of 7 kg and a radius of 5/2 m. If a point on the edge of the disk is moving at 6/5 m/s in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

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Feb 22, 2018

The angular momentum is $= 10.5 k g {m}^{2} {s}^{-} 1$ and the angular velocity is $= 0.48 r a {\mathrm{ds}}^{-} 1$

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,

$v = \frac{6}{5} m {s}^{- 1}$

$r = \frac{5}{2} m$

So,

The angular velocity is positive (spinning counter clockwise)

$\omega = \frac{\frac{6}{5}}{\frac{5}{2}} = \frac{12}{25} = 0.48 r a {\mathrm{ds}}^{-} 1$

The angular momentum is $L = I \omega$

where $I$ is the moment of inertia

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

The mass is $m = 7 k g$

So, $I = 7 \cdot {\left(\frac{5}{2}\right)}^{2} / 2 = \frac{175}{8} k g {m}^{2}$

The angular momentum is

$L = \frac{175}{8} \cdot 0.48 = 10.5 k g {m}^{2} {s}^{-} 1$

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