Physics please help.

Question

The rock is tied to a 1.5 meters string and swings in a circular path by a boy as shown. The radius of the circular path is 1.5 meters and the rock makes 100 rounds in 1 minute. The centripetal acceleration of the rock is ______ m/s^2. A. 164.3 B. 112.2 C. 168.5 D 126.3 E. 118.6.

I'm sorry it is swinging horizontally. I did not know how to upload the picture. Sorry for any inconvenience.

Answer 1

We must first calculate the stone's tangential velocity because the centripetal acceleration is given by

V²_tan / R where R is the radius of the circular motion.

As the rock makes 100 revolutions per minute, it makes one revolution in 100/60 = 1.67 revs / second.

The distance traveled during one rev is equal to the circumference of the circular path which 2π x 1.5 m =

9.42 meters. As velocity is distance per second, V = 9.42 m/rev x 1.67 rev/sec = 15.7 m/s.

The centripetal acceleration is then 15.7² m²/s² / 1.5 m = 164.3 m/s². (answer A)