Final answer:
The question involves calculating angular acceleration from applied torque, taking into account the individual moments of inertia of the drive shaft, axle, and wheels, using the principles of rotational dynamics in physics.
Step-by-step explanation:
The question relates to the topic of applied torque and angular acceleration in rotational dynamics within physics. Using the rotational equivalent of Newton's second law, we know that torque (τ) is equal to the moment of inertia (I) multiplied by the angular acceleration (α), which is stated as τ = Iα. To find the angular acceleration, we need to calculate the total moment of inertia of all the components (drive shaft, axle, and wheels) exposed to the torque and then use the given percentage of the total torque applied to these components.
For each component involved, we will calculate their moments of inertia using formulas for disks, rings, hoops, and rods:
- Disk (wheel): I = ½ m r²
- Annular ring (tire walls): I = ½ m (r1² + r2²)
- Hoop (tire tread): I = m r²
- Rod (axle and drive shaft): I = ¼ m r²
After summing all individual moments of inertia, we apply the torque to get the angular acceleration: α = τ/I. Since the problem gives the engine torque as 200 Nm, and 95% of it is used, we apply only 190 Nm (95% of 200 Nm) when calculating the angular acceleration.