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

$F = mg \rightarrow m = \frac{F}{g}$

Then,

$m = \frac{174lb}{32.17ft/s^2}$

Replacing we have then,

$(\frac{174lb}{32.17ft/s^2})\omega^2 (54ft) =174lb-146lb$

Solving to find the angular velocity we have,

$\omega = 0.309rad/s$

Therefore the angular velocity is 0.309rad/s