A solid disk, spinning counter-clockwise, has a mass of $2 k g$ $2 kg$ and a radius of $7 m$ $7 m$ . If a point on the edge of the disk is moving at $8 \frac{m}{s}$ $8 m/s$ in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

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Answer 1 · 2017-03-03T12:55:14

The angular momentum is $= 351.82 k g m^{2} s^{- 1}$ $=351.82kgm^2s^-1$
The angular velocity $= 7.18 r a d s^{- 1}$ $=7.18rads^-1$

The angular velocity is

$ω = \frac{v}{r}$ $omega=v/r$

where,

$v = 8 m s^{- 1}$ $v=8ms^(-1)$

$r = 7 m$ $r=7m$

So,

$ω = \frac{8}{7} \cdot 2 π = 7.18 r a d s^{- 1}$ $omega=(8)/(7)*2pi=7.18rads^-1$

The angular momentum is $L = I ω$ $L=Iomega$

where $I$ $I$ is the moment of inertia

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

So, $I = 2 \cdot \frac{{(7)}^{2}}{2} = 49 k g m^{2}$ $I=2*(7)^2/2=49kgm^2$

$L = 49 \cdot 7.18 = 351.82 k g m^{2} s^{- 1}$ $L=49*7.18=351.82kgm^2s^-1$

A solid disk, spinning counter-clockwise, has a mass of 2 kg2kg2 kg and a radius of 7 m7m7 m. If a point on the edge of the disk is moving at 8 m/s8ms8 m/s in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?