3. Motion in a vertical circlemg
Examine the tension in the string
when the ball is at the top. r
To find the minimum speed of the ball put T = 0
T=0 means no pull needed!

4. W = 80 N
b) Fc = W at slowest speed ie no tension felt
c) v = 2 ms-1

5. At the Bottom: Ball & String - Tension force
Examine the tension in the string
when the ball is at the bottom. r T mg

6. Motion in a vertical circle
The tension at any
point in the circle T q r q mg
top
bottom

8. Motion in a vertical circle (biker / plane ~ loop de loop?)mg
At the top: r N mg
At the bottom:
To find the minimum biking speed so that the biker feels weightlessness,
put N = 0
Biker feels heavier at the bottom

10. Is it harder for the man to hold his partner when the partner is hanging straight down and is stationary or when the partner is swinging through the straight down position?
It is harder for the man to hold his partner when the partner is swinging through.
When stationary, the man only needs to hold the force of the partner against gravity
e.g. 50kg x 9.8m/s2 = 490 N
When the partner swing, the man needs to hold with the force from gravity, PLUS the centripetal force of the partner because they are accelerating (changing v)

11. Problems:
A 150 g ball is at the end of a 1.10 m long string. It is swung in a vertical circle.
What minimum speed must the ball have to clear the top of the swing?
What tension in the string is required for the ball to move at twice the minimum speed at the bottom of its swing?
Ans: 3.28 m/s; 7.35 N

12. Vertical Circular Motion review:
An object under going vertical circle motion must satisfy the constraints of:
centripetal force to remain in a circle,
conservation of energy as Ep is converted to Ek when the mass moves up & downward.
For VCM:
Force(s) needed to provide Fc
(eg tension, normal / support forces) which is still
directed to center and constantly changing
The object speed is not necessarily constant

13. For VCM to occur:
require a combination of Forces (ΣF) eg weight, tension, lift, support forces are required to provide sufficient ΣF to keep the object moving in a circle!
unlike horizontal circles, the Forces acting on vertical circles will vary as they go around.
For uniform speed VCM ie (VUCM) to occur:
the Fc is kept constant – This means the Forces acting must vary in a particular way…
Possibly only if Forces acting are tension based !?!

14. http://www. learnerstv. com/animation/animation. php
Vertical Circular.swf

15. #1 Assume non constant speed Determine Fixed radius 10m, g = 10ms-2
Prove v = 10 ms-1 #1
Assume non
constant speed

16. #2 Determine Fixed radius 10m, g = 10ms-2 Prove v = 21.6 ms-1
Assume non
constant speed

17. #3 Determine Fixed radius 10m, g = 10ms-2 Prove v = 29.4 ms-1
Assume non
constant speed

18. #4S Assume T and W are at 90o… Determine Fixed radius 10m, g = 10ms-2
Prove v = 21.6 ms-1
#4S
Assume T and W are at 90o…
Assume non
constant speed

19. #5S T and W are not at 90o… θ =45o
Determine Fixed radius 10m, g = 10ms-2
Prove v ~ 19 ms-1
#5S
T and W are not at 90o…
θ =45o θ
Assume non
constant speed

20. #6S θ =45o Determine Fixed radius 10m, g = 10ms-2 Prove v ~ 24.5 ms-1
Assume non
constant speed

21. #7S Determine Fixed radius 10m, g = 10ms-2 Find θ = ? θ θ Assume non
constant speed θ θ

22. #8S
Solve in terms
of energy
Top
???
Assume non
constant speed
Bottom

23. Solve in terms of energy
Top
Solve in terms of energy θ
Assume non
constant speed
θ= 45o
???

25. Ex: Bicycle loop
If the radius of the loop is 2.7 m, what minimum speed must he have at the top?

27. Look at