Laser Scan
How much work is done by the motor in a CD player to make a CD spin, starting from rest? The CD has a diameter?
How much work is done by the motor in a CD player to make a CD spin, starting from rest? The CD has a diameter of 12.8 cm and a mass of 15.8 g. The laser scans at a constant tangential velocity of 1.26 m/s. Assume that the music is first detected at a radius of 20.6 mm from the center of the disk. Ignore the small circular hole at the CD’s center.
Radius of CD = R = (12.8)/2 cm = 0.064m
Momemt of Inertia of CD = MI = 0.5*m*R^2 = 0.5* 0.0158kg*(0.064)^2 = 3.24*10^-5 kg.m^2
Required initial rotational velocity = w = tangential velocity / initial radius 20.6mm
w = 1.26 / 0.0206 = 61.2 rad/s
(not taken into account by the first answer)
Work done = WD = increase in rotational kinetic energy = 0.5*MI*w^2
WD = 0.5 * 3.24*10^-5 * (61.2)^2 J
WD = 0.0605 J
(Of course in reality WD is much greater because the CD drive spindle etc. has a much greater mass than the CD itself)
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