1. Circular Motion
AP Physics C

2. Circular Motion
Uniform circular motion (constant centripetal acceleration)
Object has a circular path, constant speed.
The velocity is always tangent to the path of the object.

3. Characteristics of UniformCircular Motion
Tangential (linear) Velocity
Centripetal Acceleration
Frequency
Period

4. Speed/Velocity in a Circle
Consider an object moving in a circle around a specific origin. The DISTANCE the object covers in ONE REVOLUTION is called the CIRCUMFERENCE. The TIME that it takes to cover this distance is called the PERIOD.
Speed is the MAGNITUDE of the velocity. And while the speed may be constant, the VELOCITY is NOT. Since velocity is a vector with BOTH magnitude AND direction, we see that the direction o the velocity is ALWAYS changing.
We call this velocity, TANGENTIAL velocity as its direction is draw TANGENT to the circle.

5. Why is there acceleration in uniform circular motion?
Dv = vf – vi
a= Dv/ Dt

6. Centripetal Acceleration
Suppose we had a circle with angle, q, between 2 radaii. You may recall: Dv v
Modify for next year!! Maybe include something about similar triangles….. – this is not very clear. v vo q vo
Centripetal means “center seeking” so that means that the acceleration points towards the CENTER of the circle

7. Centripetal Acceleration
Vector
Always perpendicular to the path of the motion.
Points toward the center of the circle.
Look in book for derivation of this formula

8. Drawing the Directions correctly
So for an object traveling in a counter-clockwise path. The velocity would be drawn TANGENT to the circle and the acceleration would be drawn TOWARDS the CENTER.
To find the MAGNITUDES of each we have:

9. Frequency, f : #revolutions per unit time
f = # rev / time
Units:
(1/sec)=sec-1=Hertz (Hz)
rpm (#rev/min)
rps (#rev/sec) r

10. Period Period T : time for 1 revolution Relating Frequency and period
Unit: sec, min, h
Relating Frequency and period
f= 1 T

11. Tangential Speed in Relation to Angular Speed
Imagine you are at a rollerblading party.. You play a game where you join hands in one long chain of people and then start going in a circle… where do you want to be? Who is moving faster?
 - angular speed
Units: radians/s; rpm (rev/min)
=/t
v=r

12. Example 1
A boy whirls a stone in a horizontal circle of r=1.5m, 2m above the ground. The string breaks and the stone strikes 10m away. What was the centripetal acceleration during the circular motion?
Answer: 160m/s2

13. Examples
The blade of a windshield wiper moves through an angle of 90 degrees in 0.28
seconds. The tip of the blade moves on the arc of a circle that has a radius of 0.76m. What is the magnitude of the centripetal acceleration of the tip of the blade?

14. Circular Motion and N.S.L
Recall that according to Newton’s Second Law, the acceleration is directly proportional to the Force. If this is true:
Since the acceleration and the force are directly related, the force must ALSO point towards the center. This is called CENTRIPETAL FORCE.
NOTE: The centripetal force is a NET FORCE. It could be represented by one or more forces. So NEVER draw it in an F.B.D.

15. Examples
What is the minimum coefficient of static friction necessary to allow a penny to rotate along a 33 1/3 rpm record (diameter= m), when
the penny is placed at the outer edge of the record?
Top view FN Ff mg
Side view

16. Examples
The maximum tension that a 0.50 m string can tolerate is 14 N. A 0.25-kg ball attached to this string is being whirled in a vertical circle. What is the maximum speed the ball can have (a) the top of the circle, (b)at the bottom of the circle? T mg

17. Examples
At the bottom? T mg