A machine part has the shape of a solid uniform sphere of mass 240 g and diamete

Question

A machine part has the shape of a solid uniform sphere of mass 240 g and diameter 2.50 cm . 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 Nat that point. Part A Find its angular acceleration. Let the direction the sphere is spinning be the positive sense of rotation.(i tried to solve and i come up with 16.6 as the answer but it says it is not correct) Part B How long will it take to decrease its rotational speed by 24.0 rad/s ? A machine part has the shape of a solid uniform sphere of mass 240 g and diameter 2.50 cm . 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 Nat that point. Part A Find its angular acceleration. Let the direction the sphere is spinning be the positive sense of rotation.(i tried to solve and i come up with 16.6 as the answer but it says it is not correct) Part B How long will it take to decrease its rotational speed by 24.0 rad/s ? A machine part has the shape of a solid uniform sphere of mass 240 g and diameter 2.50 cm . 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 Nat that point. A machine part has the shape of a solid uniform sphere of mass 240 g and diameter 2.50 cm . 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 Nat that point. A machine part has the shape of a solid uniform sphere of mass 240 g and diameter 2.50 cm . 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 Nat that point. Part A Find its angular acceleration. Let the direction the sphere is spinning be the positive sense of rotation.(i tried to solve and i come up with 16.6 as the answer but it says it is not correct) Part B How long will it take to decrease its rotational speed by 24.0 rad/s ? Part A Find its angular acceleration. Let the direction the sphere is spinning be the positive sense of rotation.(i tried to solve and i come up with 16.6 as the answer but it says it is not correct) Part B How long will it take to decrease its rotational speed by 24.0 rad/s ? Part A Find its angular acceleration. Let the direction the sphere is spinning be the positive sense of rotation.(i tried to solve and i come up with 16.6 as the answer but it says it is not correct) Part B How long will it take to decrease its rotational speed by 24.0 rad/s ? Part B How long will it take to decrease its rotational speed by 24.0 rad/s ?

Explanation / Answer

a) , the formula to user here is the torque expression, stating that..

rF = I

Since I_center = 2/5 * mr², we can express the equation as...

rF = 2/5 * mr²

Solve for to get...

= F * 5/(2mr)

Therefore...

= 0.02 * 5/(2* 0.240 * 2.5 * 10^(-2)) [Note that F = 0.02 since the sphere itself cause friction.]
16.66 rad/s²

b) Use kinematics to work out the time to decrease its rotational speed to that amount..

24 =16.66t
t = 28/16.66
t 1.68 s

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