A solid disk, spinning counter-clockwise, has a mass of $1 k g$ $1 kg$ and a radius of $5 m$ $5 m$ . If a point on the edge of the disk is moving at $4 \frac{m}{s}$ $4 m/s$ in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

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Answer 1 · 2016-12-26T16:12:03

The angular momentum is $= 62.8 k g m s^{- 1}$ $=62.8kgms^(-1)$
The angular velocity is $= \frac{8 π}{5} r a d s^{- 1}$ $=(8pi)/5 rad s^(-1)$

The angular velocity is

$ω = \frac{v}{r}$ $omega=v/r$

where,

$v = 4 m s^{- 1}$ $v=4ms^(-1)$

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

So,

$ω = \frac{4}{5} \cdot 2 π = \frac{8 π}{5} r a d s^{- 1}$ $omega=4/5*2pi=(8pi)/5 rad s^(-1)$

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, $I = 1 \cdot \frac{5^{2}}{2} = \frac{25}{2} = 12.5 k g m^{2}$ $I=1*5^2/2=25/2=12.5kgm^2$

$L = 12.5 \cdot \frac{8}{5} π = 20 π = 62.8 k g m s^{- 1}$ $L=12.5*8/5pi=20pi=62.8kgms^(-1)$

A solid disk, spinning counter-clockwise, has a mass of 1kg1 kg and a radius of 5m5 m. If a point on the edge of the disk is moving at 4ms4 m/s in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?