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?

1) find speed (8.8 m/s)

2) find acceleration (38.7 m/s^2)

answer is about 38.7 m/s^2

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