The compound gear to the right is located inside a truck, whose engine rotates the driving gear with a torque of 816 N·m. Assume that in the figure to the right, each of the smaller gears have a radius of 5.0 cm, and the larger gears have a radius of 25 cm. Also, assume that the two central gears are linked by a shared axle, so that they rotate together, and that all the axles are held in place (by forces of some unknown magnitude). You may treat the gears as solid cylinders with a thickness of 2.0 cm, and a density of 8,050 kg/m3. Also, assume all the gears are moving at constant angular velocity.
a) What are the moments of inertia of both the large and small gears?
b) Using Newton's Laws, deduce the magnitude of the torque exerted by the driving gear on the large central gear, assuming that there are no additional forces/torques (other than those mentioned and gravity) acting on the driving gear.
c) Using the same reasoning as in part (b), determine the torque exerted by the smaller central gear on the large gear to the right (again assuming there are no other forces acting on the central gears). (6 pts)
d) Assuming that the driving gear is rotating at 5000 RPM, and that the large gear on the right is connected to the tires of the vehicle (30 cm radius), how fast is the truck moving (in mph)? (6 pts)