1) An engineer wishes to mountan axle on a gear (modeled as a solid disk of mass

Question

1)  An engineer wishes to mountan axle on a gear (modeled as a solid disk of mass M and radius R)to make its moment of inertia about the new axis equal to 0.563MR2. At what distance from the center of the gear shouldhe mount the axle?

Two uniform solid spheres are made fromthe same material. The larger sphere has four times the diameter ofthe smaller one. The moments of inertia about axes through theirrespective centers are I S and I L for thesmall and large spheres.

2)  The volume of a sphere is (4/3 p r 3 ). What is the value ofthe ratio I L to I S?

3)  A steam turbine is beingslowly ramped up to full speed. It starts at 1200 revolutions perminute and takes 22.5 seconds to reach 3600 revolutions per minute.Assuming it speeds up at a constant rate, how many revolutions willthe turbine make in this time?

Explanation / Answer

Moment of inertia about the axis passes through the center andperpendicular to disk

   I = ( 1/ 2) MR ^ 2

From parallel axis theorem , I ‘ = I + Mr ^ 2

                   0.563 M R ^ 2 = 0.5 MR ^ 2 + Mr ^ 2

                  0.063 R ^ 2 = r ^ 2

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