1. Class Notes for Accelerated Physics
VERTICAL CIRCLES
Class Notes for Accelerated Physics
Mr. Lyzinski
CRHS-South

2. Problems involving vertical circles (traveled at a constant velocity) are still governed by the same equations.
period (sec): frequency (Hz): tangential velocity (m/s): centripetal acceleration (m/s2): centripetal force (N):

3. HOWEVER ….. Vertical circle problems also include the effects of gravity!!!!

4. Example #1: A ball on a string swinging in Vertical Circles
What supplies the centripetal force when the ball is at the top of its path?
What supplies the centripetal force when the ball is at the bottom of its path?
What supplies the centripetal force when the ball is at the side (3 O’Clock) of its circular path?
Tension & the balls weight (together )
Forces pointing in are positive.
Tension (with the ball weight acting against it )
Tension alone (b/c the weight is not pointing into the circle)

5. Example #1: A ball on a string swinging in Vertical Circles
Assuming a constant speed:
At top:
At bottom:
Forces pointing in are positive.
If moving too fast, the string may break due to too much tension 
If moving too slow, the tension will become zero at the top (the ball will fall )

6. Example #2: A bike or car going around a Vertical –Circle LoopW FN R
How is this different from a ball on a string being swung in vertical circles?
Since the normal force is what the road “feels” (and thus the force that it pushes back with), the normal force is also the “APPARENT WEIGHT” of the bike/car. FN v
It’s the same problem, but instead of tension supplying the centripetal force, the normal force (from the track) is the supplier.
Forces pointing in are positive. W

7. A bike or car going around a Vertical-Circle loopW FN R
Assuming a constant speed:
At top: FN v
At bottom:
Forces pointing in are positive. W
If moving too slow, the car/bike will lose contact at the top and fall. Before it separates from the track, FN goes to zero! A certain speed must be maintained to avoid this.

8. “Worked-Out” Problems
1) A 5 kg ball is swung on a 1 m long rope. The rope may be assumed to be weightless. If the ball travels at a constant velocity and takes 0.5 seconds to complete a full revolution, find the tension in the rope at the top and bottom of the swing.

9. “Worked-Out” Problems
At top:
At bottom:

10. “Worked-Out” Problems
2) For the same 5 kg ball swung on the 1 m long rope, what is slowest period that will allow the ball to maintain its circular path?

11. “Worked-Out” Problems

12. “Worked-Out” Problems
A man on a motorcycle (4800 N total weight) attempts to complete a vertical circular loop of radius 3m. How fast must he be driving in order to complete the loop (Give your answer in both m/s & mph)? If he just exceeds this amount, what will be his apparent weight at the bottom of the loop?
(Assume that there is plenty of friction between the tires and the track)

13. “Worked-Out” Problems
The rider pulled 2 g’s!
(twice his weight)