Physics question #6

Question

A ball at the end of a string is swinging in a horizontal circle of radius 2.25 m. The ball makes exactly 3.00 revolutions per second. What is it’s centripetal acceleration?

Answer 1

Centripetal acceleration is given by a_c = v²/r, where v is the tangential/linear velocity, and r is the radius of the circular path.

We must find v (tangential velocity) using v = 2πr/T, where r is the radius and T is the period of the circular motion. Given that the ball travels in a circle 3 times per second, then is would take 1/3 second to travel in one rotation. (T = 1/f, where f is the frequency)

So, v = 2πr/T = 2π(2.25m)/(1/3s) = 42.4 m/s to 3 significant figures.

Thus, a_c = v²/r = (42.4m/s)²/(2.25m) = 799 m/s²