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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?

User DiegoQ
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1 Answer

1 vote

Answer:

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

User Opt
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