Torque on a spherical planetoid galaxy

[Borat321]

Hi - I had a question on webassign - here is the question.

A spherical planetoid in a galaxy far, far away has spin angular momentum of magnitude L = 5.9e+35 kg m2/s directed out of its north pole. An external torque acts on it, such that the planetoid's axis of rotation, and hence its angular momentum vector, gradually changes direction, describing a cone with half-angle 23.5 degrees as shown in the figure.
Define the y-axis as straight up in the figure (the vertical arrow shown). Define the x-axis as to the right.

Suppose the angular momentum vector takes 21200 years to swing once around the cone shown. What is the magnitude of the rate of change of the planetoid's angular momentum in that direction at the instant shown? (Hint: consider the analogy between how the component of angular momentum changes with time, and how the position of a particle in circular motion changes with time.

What is the magnitude of the external torque exerted on the planetoid?

I thoiught that the rate of cahnge of the planetoid's angular momentum can just be Lsin(23.5)w, where L=5.9e+35 and w = 2pi/21200 converted into seconds.

Also, I thought torque would just be rFsin23.5, where r = radius of Earth, but where am I going wrong?

 

[member 553083]

The rate of change of the planetoid's angular momentum in that direction would be: Lsin(23.5)w, where L is the magnitude of the spin angular momentum (5.9e+35 kg m2/s) and w is the angular velocity (2π/21200). The magnitude of the external torque exerted on the planetoid is: T = Lsin(23.5)w, where L is the magnitude of the spin angular momentum (5.9e+35 kg m2/s) and w is the angular velocity (2π/21200).