A solid disk, spinning counter-clockwise, has a mass of #8 kg# and a radius of #5/2 m#. If a point on the edge of the disk is moving at #9/4 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 · 2016-11-18T14:35:52

The angular velocity #=9/40 Hz#
The angular momentum #=45/8kgm^2s^(-1)#

First, let's calculate the angular velocity, #omega#

#omega=v/r#

#v=9/4 ms^(-1)#

#r=5/2m#

#omega=(9/4)/(5/2)=9/4*2/5=9/40 Hz#

The angular momentum, #L# is

#L=I*omega#

where, #I=#moment of inertia of the disc

Here, #I=(mr^2)/2#

#m=8 kg#

#r=5/2 m#

#I=8*25/4*1/2=25kgm^2#

So, #L=25*9/40= 45/8kgm^2s^(-1)#