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

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Answer 1 · 2017-01-04T10:23:43

The angular momentum is $= 659.7 k g m s^{- 1}$ $=659.7kgms^(-1)$
The angular velocity is $= 7.54 r a d s^{- 1}$ $=7.54rads^-1$

The angular velocity is

$ω = \frac{v}{r}$ $omega=v/r$

where,

$v = 6 m s^{- 1}$ $v=6ms^(-1)$

$r = 5 m$ $r=5m$

So,

$ω = \frac{6}{5} \cdot 2 π = \frac{12}{5} π = 7.54 r a d s^{- 1}$ $omega=6/5*2pi=12/5pi=7.54rads^-1$

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, $I = 7 \cdot \frac{{(5)}^{2}}{2} = 87.5 k g m^{2}$ $I=7*(5)^2/2=87.5kgm^2$

$L = 87.5 \cdot 7.54 = 659.7 k g m s^{- 1}$ $L=87.5*7.54=659.7kgms^(-1)$

A solid disk, spinning counter-clockwise, has a mass of 7kg7 kg and a radius of 5m5 m. If a point on the edge of the disk is moving at 6ms6 m/s in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?