Mechanics- A gyroscope question
Could somebody please explain how to do the following question?
The rotor (flywheel) of a toy gyroscope has mass 0.140 kilograms. Its moment of inertia about its axis is http://session.masteringphysics.com/...+10%5E%7B-4%7D kilogram meters squared. The mass of the frame is 0.0250 kilograms. The gyroscope is supported on a single pivot (Intro 1 figure) with its center of mass a horizontal distance 4.00 centimeters from the pivot. The gyroscope is precessing in a horizontal plane at the rate of one revolution in 2.20 seconds.
A. Find the upward force http://session.masteringphysics.com/render?var=n_vec exerted by the pivot.
B. Find the angular speed http://session.masteringphysics.com/render?var=omega at which the rotor is spinning about its axis, expressed in revolutions per minute.Give your answer in revolutions per minute to four significant figures.
For part A part A the answer I should get is (0.14+0.025)g=1.617, however, I don't see how this is correct, I understand that the only downward force is the weight and the only upward force is the normal force, but the weight acts through the centre of mass whereas the normal force acts from 4 cm away from the entre of mass.Therefore why is the normal force not mg/(4/100)?
For part B I am really stuck and any guidance would be helpful. By the way the answer you should get is http://session.masteringphysics.com/render?var=omega =1802 http://session.masteringphysics.com/...7Brev%2Fmin%7D.