Please also explain how/why the problem is solved this way :) thank you!! a popu

Question

Please also explain how/why the problem is solved this way :) thank you!!

a popular method of distributing music used to be on disks that had a radius of about 0.3m and spun at a constant angular velocity of about pi radians per second. There was a grove on the disc which mechanically shook a transducer to produce a signal. the closest it came to the center was about 0.05m so all of the information had to be stored betwwen the two radii. the longest runtime was about 22.5 minutes per side. the mass was about 0.3 kg

A. Find the tangential velocity at the inner and outer edges

B. Find the moment of inertia of a disk

D. Find the force required to stop the disk in 20 seconds applied by a finger at the outer edge

Explanation / Answer

w = pi rad/s = 3.14 rad/s

r1 = 0.05 m

r2 = 0.3 m


A) Va = r1*w = 0.157 m/s

Vb = r2*w = 0.942 m/s

B) I = (1/2)*m*(r1^2+r2^2) = 0.5*0.3*(0.05^2+0.3^3) = 0.013875 kg.m^2

C) angular acceleration, alfa = (w2-w1)/t

here w2 = 0

alfa = -3.14/20 = -0.157 rad/s^2


Torque, T = I*alfa

F*r2 = I*alfa

F = I*alfa/r2 = 0.013875*0.157/0.3 = 0.00726125 N = 7.26 m N

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