1. Vertical Circles

2. Vertical Circle
Weight is acting in the same plane as centripetal force

3. Example
A .150kg ball on the end of a 1.10 m long cord is swung in a vertical circle a) determine the minimum speed the ball must have at the top of its arc so that it continues moving in a circle b) calculate the tension of the cord at the bottom of the swing if it is moving 2x the speed calculated in part a.

4. Solution
At top of swing centripetal force is a combination of mg and FT
Fr = FT + mg
- when just keeping it in a circle, we can assume that the FT = 0 and the centripetal force is supplied only by gravity

5. At bottom, Fr = FT - mg

6. Normal Force The normal force accounts for the perception of weight
A person on a Ferris wheel moves in a vertical circle at a constant velocity. Where does the person feel the heaviest? The lightest?

8. Example
On a roller coaster, a 250kg car moves around a vertical loop of radius 15m with a speed of 13 m/s at the top of the loop and m/s at the bottom of the loop. What weight will he feel at the top and the bottom?