Answer:
The angular velocity of Ball A will be greater than the angular velocity of Ball B when they reach the top of the hill.
Explanation:
Angular velocity can be defined as how fast an object rotates relative to a given point or frame of reference.
The question said the hill encountered by Ball A is frictionless, so Ball A will continue to rotate at the same rate it started with even when it reached the top of the hill.
Ball B on the other hand rolls without slipping over its hill, i.e there's friction to slow down its rotational motion which thus reduces how fast Ball B will rotate at the top of the hill
The angular velocity of the ball B moving on a friction surface is smaller on top of the hill when compared to ball A on a frictionless surface.
The given parameters;
The angular velocity of each ball at the top of the hill is calculated by applying the principle of conservation of energy as;
[tex]\frac{1}{2} m (\omega r )^2 = mgh\\\\\omega^2 r^2 = 2mgh\\\\\omega^2 = \frac{2mgh}{r^2} \\\\\omega = \sqrt{\frac{2mgh}{r^2}} \\\\[/tex]
For the ball B moving along hill on friction surface is calculated as following;
[tex]\omega = \sqrt{\frac{\mu \ \times \ 2mgh}{r^2}}[/tex]
Thus, we can conclude that the angular velocity of the ball B moving on a friction surface is smaller on top of the hill when compared to ball A on a frictionless surface.
Learn more here:https://brainly.com/question/20432894
