Final answer:
The angular acceleration for each wheel depends on the specific conditions, including whether acceleration is possible, whether it is constant, and whether it is affected by mass inversely or directly.
Step-by-step explanation:
To determine the angular acceleration of the two wheels as they roll without slipping down inclines:
- In the case where acceleration is not possible, the angular acceleration is 0 since there is no change in velocity.
- In the case where the angular acceleration is constant, the wheels will have the same acceleration throughout the motion.
- In the case where the angular acceleration is inversely proportional to mass, the heavier wheel will have a smaller angular acceleration.
- In the case where the angular acceleration is directly proportional to mass, the heavier wheel will have a larger angular acceleration.
Using the rotational analog to Newton's second law, a = net T/I, where 'a' is the angular acceleration, 'T' is the torque exerted on the object, and 'I' is the moment of inertia. This equation is key to solving the problems presented, as it allows us to calculate angular acceleration under different constraints relating to force, mass, and the distribution of mass (moment of inertia).