In soap box car races, the cars are boxes with wheels. They begin at rest at the top of a hill, and at the start of the race the
y all begin rolling down the hill. The soap box car that reaches the bottom of the hill first is the winner. You have entered a soap box car race where the rule is that all the wheels and cars must have equal mass. Since you have taken Physics, you know that it is worse to have wheels with spokes (where the mass is mostly on the rim) rather than solid wheels because a.) The solid wheels are easier to paint.
b.) The solid wheels have a higher rotational mass or moment of inertia and therefore will retain more rotational energy.
c.) Given the same torque, the wheels with spokes have a higher rotational mass or moment of inertia and therefore will have a greater angular acceleration.
d.) Given the same torque, the wheels with spokes have a higher rotational mass or moment of inertia and therefore will have a smaller angular acceleration.
e.) Given the same amount of energy, too small a fraction is converted into rotational kinetic energy of the wheels.
Answer: D. Given the same torque, the wheels with spokes have a higher rotational mass or moment of inertia and therefore will have a smaller angular acceleration.
Explanation:
We should note that the torque is the moment of inertia multiplied by the angular acceleration. We should also realised that as the moment of inertia goes higher, the angular acceleration will be lower.
It is worse to have wheels with spokes (where the mass is mostly on the rim) rather than solid wheels because when we are given the same torque, the wheels with spokes have a higher rotational mass or moment of inertia and therefore will have a smaller angular acceleration.
