1. Dynamics of Circular Motion
Ch. 5 Applications of Newton’s Laws

2. Dynamics of Circular Motion
The net force is directed towards the center of the circular path; that is,

3. Unbanked Curve
The car to the right is going around a circular curve of radius r that is flat; that is, unbanked. The static force of friction is acting towards the center of the circular path.

4. Sample Problem
If the maximum speed of the car is 25 m/s to just maintain a circular path of 50 m, what is the coefficient of static friction?

5. Conical Pendulum
In examining the conical pendulum, you need to analyze the 2-dimensions of motion.

6. Sample Problem
If the angle is 15o and the length of the rope is 1.2 m, what is the speed of the mass to maintain this circular motion?

7. Lab 6: Conical Pendulum When pigs fly…
The purpose of this activity is to show that the net force for a conical pendulum is

8. Dynamics of Vertical Circles
When the roller coaster car and passenger are on top of the vertical circle, the net force is
When they are at the bottom of the vertical circle, the net force is

9. Dynamics of Vertical Circles-continued
When the roller coaster car and passenger are on top of the next vertical circle and upside down, the net force is

10. Sample Problem
If the total mass of the roller coaster car and the passenger is 1500 kg and the radius of the top vertical circle is 10 m, what is their speed if the passenger experiences weightlessness as they go over the top?

11. Sample Problem
As the roller coaster car and the passenger pass through the bottom of the next vertical circle, their speed is 15 m/s. Determine the force of the seat on the passenger.

12. Banked Curves

13. Sample Problem
Determine the velocity of the car to maintain its circular motion on the banked curve of 15o at a radius of 100 m.

14. Banked Curves with Friction
The "ideal" speed, videal, at which the car the car will negotiate the turn - even if it is covered with perfectly-smooth ice. Any other speed, v, will require a friction force between the car's tires and the pavement to keep the car from sliding up or down the embankment:

15. Banked Curve with Friction
v > videal (right diagram): If the speed of the car, v, is greater than the ideal speed for the turn, videal, the horizontal component of the normal force will be less than the required centripetal force, and the car will "want to" slide up the incline, away from the center of the turn. The friction force will oppose this motion and will act to pull the car down the incline, in the general direction of the center of the turn.
Write the equations applying Newton’s Second Law

16. Banked Curves with Friciton
v < videal (right diagram): If the speed of the car, v, is less than the ideal (no friction) speed for the turn, videal. In this case, the horizontal component of the normal force will be greater than the required centripetal force and the car will "want to" slide down the incline toward the center of the turn. If there is a friction force present between the car's tires and the road it will oppose this relative motion and pull the car up the incline.
Write the equations applying Newton’s second law.

17. Sample Problem
Suppose you want to negotiate a curve with a radius of 50 meters and a bank angle of 15o. If the coefficient of friction between your tires and the pavement is 0.50, what is the maximum speed that you can safely use?

18. Sample Problem
NASCAR race cars actually go through the turns at Talladega Motor Speedway at about 200 mi/hr. If that is the case, what coefficient of friction exists between the car's tires and the pavement? The radius of the turn is 1100 ft.

19. Sample Problem
Using the coefficient of static friction from the previous problem, determine the minimum speed that NASCAR race cars can actually go at through the turns at Talladega Motor Speedway.

20. Questions???