A machine part has the shape of a solid uniform sphere of mass 225 g and diamete

Question

A machine part has the shape of a solid uniform sphere of mass 225 g and diameter 4.50 cm. It is spinning about a frictionless axle through its center, but at one point on its equator, it is scraping against a metal, resulting in a frictionless force of 0.0200 N at that point. Let the direction the sphere is spinning be the positive sense of rotation.

a) Find its angular acceleration

b) How long will it take to decrease its rotational speed by 18.0 rad/s?

c) What is the maximum torque the sphere experiences?

d) What is the change in angular momentum?

Explanation / Answer

Torque T = I*alpha

I is the moment of inertia = 0.5*M*(d/2)^2 = 0.5*225*10^-3*(4.5/2)^2*10^-4 = 5.7*10^-5 kg m^2

angular accelaration alpha = T/I

Torque T = r*F = (4.5/2)*10^-2*0.02 =0.00045 N-m

alpha = T/I = 0.00045/(5.7*10^-5) = 7.9 rad/s^2

b) wf-wi = 18 rad/sec

time taken is t = (wf-wi)/alpha= 18/7.9 = 2.27 sec

C) maximum Torque is T = r*F = (4.5/2)*10^-2*0.02 =0.00045 N-m

D) change in angular momentum is dL = T*dt = 0.00045*2.27 = 0.0010215 kg m^2/sec

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