A solid disk, spinning counter-clockwise, has a mass of $5 k g$ $5 kg$ and a radius of $16 m$ $16 m$ . 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 · 2017-03-16T07:17:34

The angular momentum is $= 2010.6 k g m^{2} s^{- 1}$ $=2010.6kgm^2s^-1$
The angular velocity is $= 3.14 r a d s^{- 1}$ $=3.14rads^-1$

The angular velocity is

$ω = \frac{v}{r}$ $omega=v/r$

where,

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

$r = 16 m$ $r=16m$

So,

$ω = \frac{8}{16} \cdot 2 π = 3.1416 r a d s^{- 1}$ $omega=(8)/(16)*2pi=3.1416rads^-1$

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, $I = 5 \cdot \frac{{(16)}^{2}}{2} = 640 k g m^{2}$ $I=5*(16)^2/2=640kgm^2$

$L = 640 \cdot 3.1416 = 2010.6 k g m^{2} s^{- 1}$ $L=640*3.1416=2010.6kgm^2s^-1$

A solid disk, spinning counter-clockwise, has a mass of 5 kg5kg5 kg and a radius of 16 m16m16 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?