Question

A ball has an angular velocity of equation counterclockwise. Some time later, after rotating through a total angle of 4.5 radians, the ball has an angular velocity of equation clockwise. Determine the angular acceleration, the average angular velocity and how much time it takes for the ball to attain this velocity.

10 Feb 2026
Answer :
Word Count : 301
To solve this problem, we apply the basic equations of rotational motion. Let the initial angular velocity of the ball be (\omega_i) (counterclockwise) and the final angular velocity be (\omega_f) (clockwise). Since clockwise is opposite to counterclockwise, we take (\omega_f) as negative in our calculations. The angular displacement (\theta = 4.5 , \text{rad}). The equation connecting angular displacement, initial and final angular velocity, and angular acceleration (\alpha) is: [ \omega_f^2 = \omega_i^2 + 2 \alpha _______ _____ __________ _________ _______ _____ ________ ____ __________ _________ _____ _________.
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