A solid disk, spinning counter-clockwise, has a mass of $4 k g$ $4 kg$ and a radius of $\frac{3}{2} m$ $3/2 m$ . If a point on the edge of the disk is moving at $\frac{6}{7} \frac{m}{s}$ $6/7 m/s$ in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

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A solid disk, spinning counter-clockwise, has a mass of $4 k g$ $4 kg$ and a radius of $\frac{3}{2} m$ $3/2 m$ . If a point on the edge of the disk is moving at $\frac{6}{7} \frac{m}{s}$ $6/7 m/s$ in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

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Answer 1 · 2016-04-09T08:52:23

The moment of inertia of the disk = $I = \frac{1}{2} \times m r^{2} = \frac{1}{2} \times 4 \times {(\frac{3}{2})}^{2} = 4.5 k g m^{2}$ $I= 1/2xxmr^2=1/2xx4xx(3/2)^2=4.5kgm^2$
Angular velocity $ω = \frac{v}{r}$ $omega=v/r$ , where v = linear velocity of the poit at the age of the disk and r= radius of the disk,
Here $v = \frac{6}{7} \frac{m}{s} and r = 1.5 m$ $v=6/7m/s and r =1.5 m$
Angular velocity $ω = \frac{v}{r} = \frac{6}{7} \times \frac{1}{1.5} = \frac{4}{7} r a d s^{- 1}$ $omega=v/r=6/7xx1/1.5=4/7rads^-1$ ,
Angular momentum $= I \times ω = 4.5 \times \frac{4}{7} = \frac{18}{7} k g m^{2} s^{- 1}$ $=Ixxomega=4.5xx4/7=18/7kgm^2s^-1$

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A solid disk, spinning counter-clockwise, has a mass of $4 k g$ $4 kg$ and a radius of $\frac{3}{2} m$ $3/2 m$ . If a point on the edge of the disk is moving at $\frac{6}{7} \frac{m}{s}$ $6/7 m/s$ in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

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A solid disk, spinning counter-clockwise, has a mass of $4 k g$ $4 kg$ and a radius of $\frac{3}{2} m$ $3/2 m$ . If a point on the edge of the disk is moving at $\frac{6}{7} \frac{m}{s}$ $6/7 m/s$ in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?