Question

Suppose an automobile engine can produce 215 N⋅m of torque, and assume this car is suspended so that the wheels can turn freely. Each wheel acts like a 15 kg disk that has a 0.17 m radius. The tires act like 1.85-kg rings that have inside radii of 0.19 m and outside radii of 0.315 m. The tread of each tire acts like a 12.5-kg hoop of radius 0.33 m. The 12.5-kg axle acts like a solid cylinder that has a 1.9-cm radius. The 28-kg drive shaft acts like a solid cylinder that has a 3.05-cm radius.

Answer 1

Step 1: Calculate 95 % of 215 N.m, which is 204.25 N.m

Step 2: Calculate the moment of inertia of wheels by the formula 1/2*mr^2. Here it is 0.21675 kgm^2

Step 3: Calculate the moment of inertia of tires by the formula 1/2*(m^2+M^2). Here, it is 0.125176 kgm^2

Step 4: Calculate the moment of inertia of thread by the formula m*r^2. Here, it is 1.36125 kgm^2 

Step 5: Calculate the moment of inertia of the shaft by the formula m*r^2. Here it is 0.026047 kgm^2

Step 6: Calculate the total moment of inertia. Here it is 1.729223 kgm^2.

Step 7: Finally use this equation and solve for a(alpha) : tau = 2 * a * I (total)

Here it is 59.05831694 rad/s^2

The answer is 59.05831694 rad/s^2