Question

A machine part has the shape of a solid uniform sphere of mass 235g and diameter 2.70cm . It is spinning about a frictionless axle through its center, but at one point on its equator it is scraping against metal, resulting in a friction force of 0.0200 N at that point.

A.) Find its angular acceleration. Let the direction the sphere is spinning be the positive sense of rotation.

B.) How long will it take to decrease its rotational speed by 21.0rad/s ?

Answer 1

The relation between the torque and angular accleration is

T = I alpha

    = ( ( 2/5)mR^2) alpha

alpha = T/( 2/5)mR^2)

          = -RF/( 2/5)mR^2)

         = - F/ ( 2/5) m R

       = -0.02 N/ ( 2/5) ( 0.235 kg ) ( 2.7 * 10 ^-2 m/2)

      =-15.76 rad/s^2

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from the rotational kinematic equation

wf - wi = alphat (t)

t = wf - wi / alpha = - 21 rad/s/-15.76 rad/s^2 =1.33 s