Problem 10.7 Part A A uniform spherical shell of mass 9.00 kg with diameter 45.0

Question

Problem 10.7 Part A A uniform spherical shell of mass 9.00 kg with diameter 45.0 cm has four small masses of mass 2.00 kg attached to its outer surface and equally spaced around it. This combination is spinning about an axis running through the center of the sphere and two of the small masses (Figure 1) What friction torque is needed to reduce its angular speed from 72.0 rpm to 45.0 rpm in a time interval of 30.0 s? TE N·m SubmitMy My Answers Give Up ncorrect, Try Again; 3 attempts remaining Figure 1 Spin axis

Explanation / Answer

here,

initial angular speed , w0 = 72 rpm = 7.536 rad/s

final angular speed , w = 45 rpm

w = 4.71 rad/s

time taken , t = 30 s

let the angular accelration be alpha

w = w0 + alpha * t

4.71 = 7.536 + alpha * 30

alpha = - 0.0942 rad/s^2

mass of sphere , m1 = 9 kg

diameter , d = 45 cm

radius , r = d/2 = 22.5 cm = 0.225 m

mass attached , m2 = 2 kg

the frictional torque , T = moment of inertia * alpha

T = (2/3 * m1 * r^2 + 4 * m2 * r^2) * alpha

T = ( 2/3 * 9 * 0.225^2 + 4 * 2 * 0.225^2) * 0.0942 N.m

T = 0.3 N.m

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