A solid disk, spinning counter-clockwise, has a mass of $12 k g$ $12 kg$ and a radius of $6 m$ $6 m$ . If a point on the edge of the disk is moving at $2 \frac{m}{s}$ $2 m/s$ in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

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Answer 1 · 2016-11-28T11:06:19

The angular velocity $= \frac{1}{3} H z$ $=1/3 Hz$
The angular momentum is $= 72 k g m s^{- 1}$ $=72kgms^(-1)$

The angular velocity is

$ω = \frac{v}{r}$ $omega=v/r$

Where $v = v e l o c i t y = 2 m s^{- 1}$ $v=velocity=2ms^(-1)$

and $r = r a d i u s = 6 m$ $r=radius=6m$

So, $ω = \frac{2}{6} = \frac{1}{3} H z$ $omega=2/6=1/3Hz$

The angular momentum is

$L = I ω$ $L=Iomega$

Where, $I =$ $I=$ moment of inertia

The moment of inertia of a solid disc is $= \frac{m r^{2}}{2}$ $=(mr^2)/2$

where, $m =$ $m=$ mass of the disc

$I = 12 \cdot 6 \cdot \frac{6}{2} = 216 k g m^{2}$ $I=12*6*6/2=216kgm^2$

and $L = 216 \cdot \frac{1}{3} = 72 k g m s^{- 1}$ $L=216*1/3=72kgms^(-1)$

A solid disk, spinning counter-clockwise, has a mass of 12kg12 kg and a radius of 6m6 m. If a point on the edge of the disk is moving at 2ms2 m/s in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?