Download Vertical Circles and Curves

Vertical Circles
Vertical Circle

Weight is acting in the same plane as
centripetal force
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.
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


At bottom, Fr = FT - mg
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?

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 22 m/s at the bottom of the loop.
What weight will he feel at the top and
the bottom?