An automobile engine can produce 200 N · m of torque. Calculate the angular acceleration produced if 95.0% of this torque is applied to the drive shaft, axle, and rear wheels of a car, given the following information. The car is suspended so that the wheels can turn freely. Each wheel acts like a 15.0 kg disk that has a 0.180 m radius. The walls of each tire act like a 2.00-kg annular ring that has inside radius of 0.180 m and outside radius of 0.320 m. The tread of each tire acts like a 10.0-kg hoop of radius 0.330 m. The 14.0-kg axle acts like a rod that has a 2.00-cm radius. The 30.0-kg drive shaft acts like a rod that has a 3.20-cm radius.
Step-by-step solution Step 1 of 4 For the angular acceleration, first find out the moment of inertia of all the parts individually and adding them to find out the total moment of inertia of the system and net torque. Step 2 of 4 Moment of inertia of the wheel (disc) about its axis is, so the moment of inertia of a wheel (disc) is, Here is the mass of the wheel and is the radius of the wheel, Substitute and Moment of inertia for the walls of tires, suppose walls of tire as annular ring, Here is the inner radius of the walls and is the outer radius, is the mass of the wall. Substitute, and ,