1. Vertical Circles

2. Consider a 1-kg brick being whirled in a vertical circle at the end of a 1-meter rope.
What critical velocity must the brick achieve in order to pass safely through the top of its circular path?
If it continues to go at this speed (unlikely), then what would be the tension at the bottom of the path?

3. A 60 kg person is riding a roller coaster through a circular section of the track, a "loop-the-loop" with radius 10m.
Find the speed of the rider if he just makes it around the top of the curve.
What is the value of the normal force at the top if he’s going 10m/s more?
Going at this speed, what is the normal force he experiences at the bottom of the loop?

4. While driving to work you pass over a "crest" in the road that has a radius of 30 m.
How fast would you need to be traveling to experience apparent "weightlessness" while passing over the crest?

5. A student is riding on The American Eagle at Great America
A student is riding on The American Eagle at Great America. The student is moving at 18.9 m/s over the top of a hill which has a radius of curvature of 12.7 m. Use Newton's second law to determine the magnitude of the applied force of the track pulling down upon the student's 621 kg roller coaster car.

6. A bucket of mass 1. 80 kg is whirled in a vertical circle of radius 1
A bucket of mass 1.80 kg is whirled in a vertical circle of radius 1.50 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N.
Find the speed of the bucket.
How fast must the bucket move at the top of the circle so that the rope does not go slack?

7. Sources