A solid disk, spinning counter-clockwise, has a mass of $7 k g$ $7 kg$ and a radius of $\frac{8}{3} m$ $8/3 m$ . If a point on the edge of the disk is moving at $\frac{1}{4} \frac{m}{s}$ $1/4 m/s$ in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

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Answer 1 · 2017-06-13T13:56:27

The angular momentum is $= 2.33 k g m^{2} s^{- 1}$ $=2.33kgm^2s^-1$ and the angular velocity is $= 0.09375 r a d s^{- 1}$ $=0.09375rads^-1$

The angular velocity is

$omega=(Deltatheta)/(Deltat)$

$v=r*((Deltatheta)/(Deltat))=r omega$

$omega=v/r$

where,

$v=1/4ms^(-1)$

$r=8/3m$

So,

$omega=(1/4)/(8/3)=3/32=0.09375rads^-1$

The angular momentum is $L=Iomega$

For a solid disc, $I=(mr^2)/2$

So, $I=7*(8/3)^2/2=224/9kgm^2$

The angular momentum is

$L=224/9*3/32=7/3=2.33kgm^2s^-1$

A solid disk, spinning counter-clockwise, has a mass of 7 kg7kg7 kg and a radius of 8/3 m83m8/3 m. If a point on the edge of the disk is moving at 1/4 m/s14ms1/4 m/s in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?