A turntable must spin at 33.3 rpm to play an old-fashioned vinyl record. The tur

Question

A turntable must spin at 33.3 rpm to play an old-fashioned vinyl record. The turntable is a uniform disk of radius 15 cm and mass 0.16 kg. How much constant torque (in N.m) must the motor deliver if the turntable is to reach its final angular speed in 2.5 revolutions, starting from rest? (1) 6.97 x 10^-4 (2) 1.16 x 10^-3 (3) 8.71 x 10^-4 (4) 2.37 x 10^-3 (5) 4.65 x 10^-4 In the previous problem, how much work (in mJ) must the motor do if the turntable is to reach its final angular speed in 2.5 revolutions, starting from rest? (1) 10.9 (2) 8.5 (3) 5.4 (4) 21.8 (5) 2.9

Explanation / Answer

Wf^2 = Wi^2 + 2a*theta

3.4854^2 = 2*a*(2.5*2pi)

a = 0.39 rad/sec^2

T = Ia = 1/2MR^2*a = 1/2*0.16*0.15^2*0.39 = 0.000696 Nm

So correct option is a) 6.97*10-4 Nm (ans)

b) Energy= 1/2 *I*w^2 = 1/2*1/2MR^2*w^2 = 0.0109 J = 10.9 mJ

So correct option is 1) 10.9 mJ (ans)

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