An amusement park ride spins its occupants in a circle with a radius of 2.30 m. how many revolutions per minute does the ride need to spin at if the riders feel a centripetal acceleration equal to that of the earth’s gravity?

11.67 revolutions per minute

Explanation:

Centripetal acceleration a  =  r ω ²

Where, ω  is angular velocity.

From the question, centripetal acceleration equal to that of the earth’s gravity

                                      g  =  r ω ²

substituting the values of acceleration due to gravity g and radius r                                      

                                   9.8 = 2.30 x ω ²

                                   ω ² =

                                   ω ² = 4.261

                                   ω  =

                                   ω  = 2.06 rad/second

Angular velocity ω =

where T is the period ⇒ time taken to complete one revolution

Substituting the calculated value of ω into the equation to solve for period T

                                    2.06   =

                                    T =

                                    T = 3.05 seconds

The revolutions per minute =

                                             = 11.67 revolutions per minute