At what rate on a Ferris wheel would a person feel there true weight?

Question

I'm pretty sure I use the formula
square root of radius * gravity...but what else am I missing?

Answer 1

Assuming the Ferris wheel is on earth and not in space(!), they would only feel their true weight if the Ferris wheel is not moving at all. If the Ferris wheel is moving, they'll feel a little heavier than true weight at the bottom, and a little lighter than true weight at the top.

But I think your formula, v = sqrt(r&moddot;g), is on the right track. At that speed, the rider is experiencing a centripetal acceleration equal to "g". But when you factor in the force of gravity, the result of going that speed would be:

* At the bottom of the wheel, the person would feel TWICE their weight (if they weighed 150 lbs, they'll feel like 300 lbs);
* At the top of the wheel, they'll feel zero weight (i.e., they'll feel weightless).

Say the wheel is 100 ft. in radius. That would correspond to a speed of 39 mph, or a revolution time of about 11 sec -- pretty fast for a Ferris wheel.