A solid disk, spinning counter-clockwise, has a mass of $15 k g$ $15 kg$ and a radius of $4 m$ $4 m$ . If a point on the edge of the disk is moving at $7 \frac{m}{s}$ $7 m/s$ in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

Question

1392 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-22T11:16:27

The angular momentum is $= 1320 k g m s^{- 1}$ $=1320kgms^(-1)$
The angular velocity is $= 11 r a d s^{- 1}$ $=11rads^-1$

The angular velocity is

$ω = \frac{v}{r}$ $omega=v/r$

where,

$v = 7 m s^{- 1}$ $v=7ms^(-1)$

$r = 4 m$ $r=4m$

So,

$ω = \frac{7}{4} \cdot 2 π = \frac{7}{2} π = 11 r a d s^{- 1}$ $omega=7/4*2pi=7/2pi=11rads^-1$

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, $I = 15 \cdot \frac{{(4)}^{2}}{2} = 120 k g m^{2}$ $I=15*(4)^2/2=120kgm^2$

$L = 11 \cdot 120 = 1320 k g m s^{- 1}$ $L=11*120=1320kgms^(-1)$

A solid disk, spinning counter-clockwise, has a mass of 15kg15 kg and a radius of 4m4 m. If a point on the edge of the disk is moving at 7ms7 m/s in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?