Question

A 174 pound Jimmy Cheek is riding on a 54 ft diameter Ferris Wheel. The normal force on Jimmy Cheek is 146 pounds when Jimmy is at the top of the wheel. Determine the angular velocity of the Ferris Wheel.

Answer 1

To solve this problem we will apply the concepts related to the balance of Forces, the centripetal Force and Newton's second law.

I will also attach a free body diagram that allows a better understanding of the problem.

For there to be a balance between weight and normal strength, these two must be equivalent to the centripetal Force, therefore

`F_c = W-N`

`m\omega^2r = W-N`

Here,

m = Net mass

`\omega`= Angular velocity

r = Radius

W = Weight

N = Normal Force

`m\omega^2r = 174-146`

The net mass is equivalent to

`F = mg \rightarrow m = (F)/(g)`

Then,

`m = (174lb)/(32.17ft/s^2)`

Replacing we have then,

`((174lb)/(32.17ft/s^2))\omega^2 (54ft) =174lb-146lb`

Solving to find the angular velocity we have,

`\omega = 0.309rad/s`

Therefore the angular velocity is 0.309rad/s