1. Circular Motion; Gravitation
Chapter 5
Circular Motion; Gravitation

2. Units of Chapter 5 Kinematics of Uniform Circular Motion
Dynamics of Uniform Circular Motion
Highway Curves, Banked and Unbanked
Nonuniform Circular Motion
Centrifugation
Newton’s Law of Universal Gravitation
Gravity Near the Earth’s Surface; Geophysical Applications
Satellites and “Weightlessness”
Kepler’s Laws and Newton’s Synthesis
Types of Forces in Nature

3. Objectives: The student will be able to:
identify uniform circular motion.
determine the directions of the velocity and acceleration vectors for an object in uniform circular motion.
calculate the centripetal acceleration of a point mass in uniform circular motion given the radius of the circle and either the linear speed or the period of the motion.
state the relationship between the period of the motion and the frequency of rotation and express this relationship using a mathematical equation.

4. Uniform Circular Motion: Definition
Constant speed, or,
constant magnitude of velocity
Motion along a circle:
Changing direction of velocity
April 23, 2017

5. Uniform Circular Motion
Uniform circular motion is motion along a circular path in which there is no change in speed, only a change in direction.
Constant velocity tangent to path. v Fc
Constant force toward center.
Question: Is there an outward force on the ball?

6. Uniform Circular Motion (Cont.)
The question of an outward force can be resolved by asking what happens when the string breaks!
Ball moves tangent to path, NOT outward as might be expected. v
When central force is removed, ball continues in straight line.
Centripetal force is needed to change direction.

7. 5-1 Kinematics of Uniform Circular Motion
Uniform circular motion: motion in a circle of constant radius at constant speed
Instantaneous velocity is always tangent to circle.

8. 5-1 Kinematics of Uniform Circular Motion
This acceleration is called the centripetal, or radial, acceleration, and it points towards the center of the circle.

9. Examples of Centripetal Force
You are sitting on the seat next to the outside door. What is the direction of the resultant force on you as you turn? Is it away from center or toward center of the turn? Fc
Car going around a curve.
Force ON you is toward the center.

10. Car Example Continued F’ Fc
The centripetal force is exerted BY the door ON you. (Centrally) F’
Reaction Fc
There is an outward force, but it does not act ON you. It is the reaction force exerted BY you ON the door. It affects only the door.

11. Another Example

12. Spin Cycle on a Washer
How is the water removed from clothes during the spin cycle of a washer?
Think carefully before answering Does the centripetal force throw water off the clothes?
NO. Actually, it is the LACK of a force that allows the water to leave the clothes through holes in the circular wall of the rotating washer.

13. Centripetal Acceleration
Consider ball moving at constant speed v in a horizontal circle of radius r at end of string tied to peg on center of table. (Assume zero friction.) n Fc r v W
Force Fc and acceleration ac toward center. W = n

14. Deriving Central Acceleration
Consider initial velocity at A and final velocity at B: vf vf B r vo
-vo Dv r vo s A
S is the length of the arc.

15. Deriving Acceleration (Cont.)vf
-vo r vo Dv s
ac = Dv t
Definition: = Dv v S r
Similar Triangles
mass m = Dv t Vs rt
ac = = Vv r
s/t is equal to velocity
Centripetal acceleration:

16. Example 1: A 3-kg rock swings in a circle of radius 5 m
Example 1: A 3-kg rock swings in a circle of radius 5 m. If its constant speed is 8 m/s, what is the centripetal acceleration? r v m
m = 3 kg
r = 5 m; v = 8 m/s
F = (3 kg)(12.8 m/s2)
Fc = 38.4 N

17. Period and Frequency
A circular motion is described in terms of the period T, which is the time for an object to complete one revolution.
The distance traveled in one revolution is r
The frequency, f, counts the number of revolutions per unit time.

18. Example of Uniform Circular Motion
Example 5-2 in text
The moon’s nearly circular orbit about the earth has a radius of about 384,000 km and a period T of 27.3 days. Determine the acceleration of the Moon towards the Earth.

19. Homework
Questions p.129
#s 1, 10
Problems
#s 1, 3, 5

20. Closure
Kahoot Section 5-1 Giancoli