Final answer:
The moment of inertia of an engine's flywheel is constant regardless of rotational speed and is dependent on mass distribution, not on the speed of rotation. An increase in momentum of inertia results in a decrease in angular velocity due to the conservation of angular momentum.
Step-by-step explanation:
The moment of inertia of an engine's flywheel about its rotation axis remains constant regardless of rotational speed. The moment of inertia is a property that measures the resistance of a body to change its state of rotation and is solely dependent on the mass distribution relative to the rotation axis, not on the speed of rotation.
When the moment of inertia of an isolated system increases, the angular velocity of the system decreases. This is due to the conservation of angular momentum, which is the product of moment of inertia and angular velocity. If no external torques act on the system, the angular momentum remains constant. Therefore, if the moment of inertia goes up, the angular velocity must go down to keep the angular momentum unchanged.
Considering a child getting off a merry-go-round, the angular velocity of the merry-go-round will behave as follows:
- (a) If he jumps off radially, the angular velocity remains the same as angular momentum is conserved.
- (b) Jumps backward to land motionlessly, the merry-go-round's angular velocity increases.
- (c) Jumps straight up and hangs onto an overhead tree branch, the angular velocity decreases since the system's moment of inertia increases.
- (d) Jumps off forward, tangential to the edge, the angular velocity of the merry-go-round increases since the system’s moment of inertia decreases.