# Homework Help: Rotational motions

1. Nov 30, 2005

### furtivefelon

there are two challange questions i don't quite understand what they are saying..

1. A horizontal plate with mass M lies on two rotating cylinders with equal angular speed of roation, but opposite directions of rotation. The distance between the axes of cylinders is l. The coefficient of kinetic friction between the plate and the material of the cylinders is u (not sure how to input the coefficient of friction)
a) Prove that the plate initially at the equilibrium position will start the harmonic oscillation if it is slightly displaced from the equilibrium in horizontal direction
b) Find the frequency of the oscillations
c) What is the result of hte same displacement if the angular velocities have opposite directions

Ok, for the first queston, i don't understand how the wheel rolling could start an oscillation.. hopefully i had hte attachments right, if so, then i have attached the diagram they provided..

2. A spacecraft with mass Mo (subscript) is moving with constant velocity Vo in free space. To change its direction the maneuvering jet engine is turned on, which starts to eject fuel at a constant velocity u relative to the spacecraft. During the maneuver, vectors Vo and u are always mutually perpendicular. Finally, the mass of the spacecraft becomes m.

Find the angle between the initial and final direction of motion of the spacecraft

for the second question, when they say one mass becomes another mass, do they mean the final mass after the fuel has been ejected? or do i need special relativity..

thanks alot for answering :D If there is any other hints you may give me, it would be highly appreciated :D

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