Answer:
(a). The magnitude of the total acceleration of the ball is 239.97 m/s².
(b). The angle of the total acceleration relative to the radial direction is 11.0°
Explanation:
Given that,
Radius of the circle = 0.681 m
Angular acceleration = 67.7 rad/s²
Angular speed =18.6 rad/s
We need to calculate the centripetal acceleration of the ball
Using formula of centripetal acceleration

Put the value into the formula


We need to calculate the tangential acceleration of the ball
Using formula of tangential acceleration

Put the value into the formula


(a). We need to calculate the magnitude of the total acceleration of the ball
Using formula of total acceleration

Put the value into the formula


(b). We need to calculate the angle of the total acceleration relative to the radial direction
Using formula of the direction

Put the value into the formula


Hence, (a). The magnitude of the total acceleration of the ball is 239.97 m/s².
(b). The angle of the total acceleration relative to the radial direction is 11.0°