Motion in a Vertical Circle (Pendulum)

[cturtle]

Homework Statement

A bowling ball weighing 71.2 N is attached to the ceiling by a 3.80m rope. The ball is pulled to one side and released. It then swings back and forth like a pendulum. As the rope swings through its lowest point, its speed is 4.20 m/s. At that instant, find a) the magnitude and direction of the acceleration of the bowling ball and b) the tension of the rope.


2. The attempt at a solution

I used a_c= V²/r
to find the acceleration, 4.6 m/s². I know what magnitude and direction are, but I'm stumped on how to find them. Do I just use the rope as the y component? If so, how do I find an angle? I think I know how to do part b, but help there would be appreciated too! Thanks for your help!

 

[fluidistic]

I think I know how to do part b, but help there would be appreciated too! Thanks for your help!

The tension is equal to the centripetal force plus the weight of the ball.
As for part a), when the ball reaches its lowest point, there is no tangential acceleration but a centripetal one. The direction is simply the center of the circular path that describe the ball.