A steady 4.0-lb force is applied normal to the handle of the hand-operated grinder. The gear inside the housing with its shaft and attached handle together weigh 4.26 lb and have a radius of gyration about their axis of 2.97 in. The grinding wheel with its attached shaft and pinion (inside housing) together weigh 1.07 lb and have a radius of gyration of 1.95 in. If the gear ratio between gear and pinion is 5:1, calculate the speed N (in revolutions/min) of the grinding wheel after 5 complete revolutions of the handle starting from rest.

the speed N of the grinding wheel after 5 complete revolutions of the handle starting from rest is 3122.62 rev/min

Explanation:

From the given information ;

According to the principles of Conservation of energy;

where;

gain in potential energy as a result of restoring friction

= kinetic energy as a result of rotation of the gear housing

= Kinetic energy as a result of rotation of pinion housing

However; the equation can be re-written as:

where;

F = restoring Force

I = mass moment of the inertia

r = radius of gyration

Let assume the mass moment of inertia is 6.0 In around the the handle of the hand-operated grinder,  since it is not given and a diagram is not attached ;

NOW;

62.83 =

62.83 =

The spinning of the wheel is

N = 3122.62 rev/min

Thus; the speed N of the grinding wheel after 5 complete revolutions of the handle starting from rest is 3122.62 rev/min