Question

A ball is tied to the end of a cable of negligible mass. The ball is spun in a circle with a radius 2.00 m making 0.700 revolutions per second. What is the centripetal acceleration of the ball?

Answer 1

Centripetal acceleration = (speed)²/(radius) .

We know the radius.  We have to find the speed.

Speed around a circle = (circumference) / (time to go around)

The circumference of the circle is  (2 π) (radius) = 4 π meters.

We don't exactly know the time to go around.
We know that the ball goes around 0.7 times/second.
Flip that over, and you have  time to go around = second/0.7 .

So now, the centripetal acceleration is

                                   (speed)²/(radius) .

                             =  (4π meters · 0.7/sec)² / (2 meters)

                             =  (4π · 0.7 / 2)    m/s²

                             =      about        4.4 m/s²

Answer 2

1) find speed (8.8 m/s)
2) find acceleration (38.7 m/s^2)
answer is about 38.7 m/s^2