1. Vertical Circular Motion

2. Roller Coaster

3. Roller Coaster

4. Twirling a Ball on a String Verticallyx mg T T mg
maR
T = 0; vcr mg
maR
T cannot be negative, the bob will fall down! mg
maR

5. Non-uniform Circular Motion
If an object is moving in a circular path but at varying speeds, it must have a tangential component to its acceleration as well as the radial one.

6. Ferris Wheel

7. Sustained vertical spinning
Ever wonder what a bike tire feels like?
At constant speed, the centripetal acceleration is constant (v2/r), but the direction of gravity keeps changing!
Feel heavier at bottom than at top
This ride definitely turns your world around!

8. Bucket of Water
NB,W
water a
WE,W

9. Bridges & Speed Bumps
The curvature of the bridge/bump and your speed determines if you are going to stay on the bump (N>0) or if you are going to bump: fly off it!

10. How fast do you need to drive to leave the ground?

11. Connected Bodies
Two different masses (m < M) are connected by a string going through a tube. Predict what will happen when you whirl the lighter mass with constant but high speed. Base your prediction on the CM model. m M
Mass M will be falling down since it is heavier
Mass M will be moving up and then stop
Mass M will move up and then will fall down
It is impossible to whirl the lighter mass around

12. Connected Bodies - Analysisq m M T mg x y
If the mv2/R is > Mg, the mass M will accelerate upwards. Notice, the mass m will always rotate so the string is not horizontal. It happens so T has a vertical component to cancel out the mg!

13. Satellites in Circular Orbits

14. Weightlessness in Space Shuttle

15. Artifical Gravity