Refer to question below

Question

While bowling a cricket ball, Carl Spackler holds the ball 0.9m from the axis of rotation at his shoulder. The movement takes 0.42s and, at the moment of release, the ball has a tangential linear velocity of 40m/s and an angular acceleration of 120rad/s^2.

a) What are the magnitudes of the tangential and centripetal accelerations at release?

b) What is the magnitude of the resultant acceleration of the ball?

Answer 1

a) acceleration _centripetal = v² /r (at moment of release) = 40²/.9=1778 m/s

a) acceleration _tangential = (angular acceleration) * radius = 120*.9 = 108 m/s

b) acceleration _resultant = sqrt(a_c²+a_t²) = sqrt(1082+17782)= 1781 m/s