Question

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?

Answer 1

11.67 revolutions per minute

Step-by-step 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 =
`(9.8)/(2.30)`

ω ² = 4.261

ω =
`√(4.261)`

ω = 2.06 rad/second

Angular velocity ω =
`(2\pi )/(T)`

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 =
`(2\pi )/(T)`

T =
`(2\pi )/(2.06)`

T = 3.05 seconds

The revolutions per minute =
`(60)/(3.05)`

= 11.67 revolutions per minute