session.masteringphysics.com Lafayette Physics 131 - Spring 2016 - Boekelheide a

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session.masteringphysics.com Lafayette Physics 131 - Spring 2016 - Boekelheide and Plenge Signed in as Kurt Bringsjord Help Close Homework #12 Problem 10.56 Resources «previous 8 of 11 next » Problem 10.56 Part A A uniform spherical shell of mass 8.40 kg with diameter 53.0 cm has four small masses of mass 2.50 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 70.0 rpm to 45.0 rpm in a time interval of 27.0 s? -8.878-10- Submit My Answers Give Up Figure 1 of 1 Incorrect Try Again; 9 attempts remaining Spin axis Provide Feedback Continue

Explanation / Answer

shell moment of inertia:

Is = (2/3) M R^2 = (2/3) * (8.4) * (0.53/2)^2 = 0.39326 kg.m^2

total moment of inertia:

I = Is + 2 m R^2 = 0.39326 + (2) * (2.50) * (0.53/2)^2 = 0.744385 kg.m^2

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angular acceleration:

alpha = (45-70)*(2*3.1416/60)/(27) = -0.09696 rad/s^2

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torque:

tau = I alpha = (0.744385) * (-0.09696) = -0.072 N.m

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