A machine part has the shape of a solid uniform sphere of mass 205 and diameter

Question

A machine part has the shape of a solid uniform sphere of mass 205 and diameter 3.70 . 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 at that point. 1)Find its angular acceleration. Let the direction the sphere is spinning be the positive sense of rotation. 2)How long will it take to decrease its rotational speed by 19.0 ? I attempt it and i got 6.60 for question one. but I am wrong..

Explanation / Answer

a) Then, the formula to user here is the torque expression, stating that.. rF = Ia Since I_center = 2/5 * mr², we can express the equation as... rF = 2/5 * mr²a Solve for a to get... a = F * 5/(2mr) Therefore... a = 0.02 * 5/(2* 0.205 * 3.9 * 10^(-2)) [Note that F = 0.02 since the sphere itself cause friction.] ˜ 6.25 rad/s² b) Use kinematics to work out the time to decrease its rotational speed to that amount... The frequency/radians is not given here, so I would assume that... 28 = 6.25t t = 28/6.25 t ˜ 4.48 s Good luck!

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