A solid sphere of mass m and radius r spins about a horizontal axis with period

Question

A solid sphere of mass m and radius r spins about a horizontal axis with period T. It is hung by a thread attached to that horizontal axis at the edge of the sphere.

A.) Find the size and direction of the angular momentum L (vector) of the sphere spinning about its axis relative to the string and the axis of rotation.

B.) Find the size of the torque acting on the sphere about the string.

C.) Find the direction of the torque relative to the direction of the angular momentum.

D.) Can a torque in this direction change the size of the angular momentum? What shape does the tip of the angular momentum vector make if you follow it over time?

E.) Recall that for an arc length (delta s)subtended by an angle (delta theta), the equation (delta theta) = (delta s)/r leads to the equation (omega) = (v final)/r. By analogy to that, find the angular velocity of the precession, (omega_p vector), of the spinning sphere. N.B.: This angular velocity is not the angular velocity obtained by 2pi/T.

Thanks for the help in advance!

Explanation / Answer

it is very difficult to visualize the problem without the figure. Please provide the figure. By the way.... torque and momentum doesn't have a size, they have a magnitude.... just sayin'

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