1. Uniform Circular Motion Chapter 5 Lesson 1

2. 5.1 Uniform Circular Motion
Object is traveling at a constant (uniform) speed on a circular path
Period (T) – Time it takes to make one trip around the circle
Circumference – distance around the circle
C = 2r

3. Uniform Circular Motion
Speed (v) – distance / time
Find v
v = 3.77 m/s
1.2 m
Work on board
v = 2r / T  v = 2(1.2m)/2s  v = 2.4m /2s = 3.77 m/s
T=2s

4. Uniform Circular Motion
Speed is constant
Velocity is not constant
Velocity is always changing
This acceleration is “centripetal” acceleration

5. 5.2 Centripetal Acceleration
Object moves in circular path
At time t0 it is at point O with a velocity tangent to the circle
At time t, it is at point P with a velocity tangent to the circle
The radius has moved through angle 

6. Centripetal Acceleration
Draw the two velocity vectors so that they have the same tails.
The vector connecting the heads is v
Draw the triangle made by the change in position and you get the triangle in (b)

7. Centripetal Acceleration
Since the triangles have the same angle are isosceles, they are similar

8. Centripetal Acceleration

9. Centripetal Acceleration
Know this

10. Centripetal Acceleration
At any given moment
v is pointing tangent to the circle
ac is pointing towards the center of the circle
If the object suddenly broke from circular motion would travel in line tangent to circle
Have a string with something soft on end.
Swing it and let go to illustrate.

11. Example 1
Two identical cars are going around two corners at 30 m/s. Each car can handle up to 1 g. The radius of the first curve is 50m and the radius of the second is 100 m. Do either of the cars make the curve? (hint find the ac)
Yes, 100m
ac1 = v2/r  ac1 = (30 m/s)2/50m  ac1 = 18 m/s2 Can’t make it
ac2 = (30 m/s)2/100m = 9 m/s2 Yes
50 m
100 m

12. Example 5-1
A 150 kg ball at the end of a string is revolving uniformly in a horizontal circle of radius m. The ball makes 2.00 revolutions in a second. What is its centripetal acceleration?

13. Example 5-2
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 toward the earth.

14. What is Centripetal Force?

15. 5-2 Dynamics of Uniform Circular Motion
For an object to be in uniform circular motion, there must be a net force acting on it.
We already know the acceleration, so can immediately write the force:
(5-1)
We can see that the force must be inward by thinking about a ball on a string:

16. Directions in centripetal force problems:
Positive direction is inwards toward center of circle.
Negative direction is outward away from center of circle.

17. 5-2 Dynamics of Uniform Circular Motion
There is no centrifugal force pointing outward; what happens is that the natural tendency of the object to move in a straight line must be overcome.
If the centripetal force vanishes, the object flies off tangent to the circle.

18. Example 5-3
Estimate the force a person must exert on a string attached to a kg ball to make the ball revolve in a horizontal circle of radius m. The ball makes 2.00 revolutions per second (T=0.500 s).

19. To Be Continued…