Question

A merry-go-round has a period of 0.64 seconds. Its radius is 1.8 meters. What is its centripetal acceleration?

Answer 1

The centripetal acceleration is 172 m /s^2.

Explanation:

The acceleration that causes an object to move along a circular path, or turn is known as the centripetal acceleration. Centripetal acceleration points radially inward from the object's position and making a right angle with the object's velocity vector.

The centripetal acceleration is given as

                                Ac = v^2 / r

where Ac represents the centripetal acceleration of an object.

          v represents the linear velocity

           r represents the radius of rotation.

Given t = 0.64 s,    r = 1.8 m.

To find linear velocity, v = (2 * pi * r) / t

                                         = (2 * 3.14 * 1.8) / 0.64

                                     v  = 17.6 m / s.

Centripetal acceleration = v^2 / r

                                           = (17.6 * 17.6) / 1.8

                                           = 172 m / s^2.