1. Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 30-32 Hw: Chapter 13 problems and exercises Reading: Chapter 14

2. Polar coordinates

3. A ball of mass m is swung around a circle at the end of a string of length L. The string will break if the tension in it exceeds a critical value, T c. What is the largest constant angular velocity the ball can have without breaking the string?

4. Quiz Suppose a particle of mass m is attracted to the origin with a force proportional to the inverse square of the distance to the origin, r: Calculate the work done by this force: a) if the particle moves from A to B where A and B are points on a circle, centered at the origin; b) If the particle moves out along a radius vector from B (r B from the origin) to C (r C from the origin).

5. A mass M is going around in a circle on a string on a frictionless table and the string goes through a hole where it is attached to a hanging mass m. If the mass M is going around with constant, what must the distance from the mass M to the hole be if the mass m is to remain at rest? M m

6. Platform rotates with angular acceleration  (t)=  t. A man starts a distance L from the center and walks in along a straight line painted on the platform towards the center. He decreases his distance from the center as a constant rate, v c. What force does the platform exert on the man, as a function of his distance from the center?

7. A plane is flying in an arc at the speed of v 0. At the top of arc the passengers experience a sense of weightlessness. What is the radius of the arc?

8. Conical pendulum

9. A race track designer wants to have the cars able to maintain a speed v max without skidding on a circular track. If the track is flat with a coefficient of friction  what does the radius have to be?

10. H R A frictionless track contains a circular section of radius R as shown. What is the minimum height at which a block must be started in order for it to go around the loop without falling off the track?

12. Have a great day! Hw: Chapter 13 problems and exercises Reading: Chapter 14