1. Uniform Circular Motion

2. Uniform circular motion
motion of an object in a circle with a constant or uniform speed
constant change in direction

3. Uniform Circular Motion: Period
Object repeatedly finds itself back where it started.
The time it takes to travel one “cycle” is the “period”.

4. Quantifying Acceleration: Magnitudev1 v2

6. Quantifying Acceleration: Magnitude

7. Applying Newton’s 2nd Law:
Centripetal Force
Always points toward center of circle. (Always changing direction!)
Centripetal force is the magnitude of the force required to maintain uniform circular motion.

8. Direction of Centripetal Force, Acceleration and Velocity
Without a centripetal force, an object in motion continues along a straight-line path.

9. Direction of Centripetal Force, Acceleration and Velocity

10. The force or forces needed to bend the normally straight path of a particle into a circular or curved path is called the
It is a pull on the body and is directed toward the center of the circle.
CENTRIPETAL FORCE.
Tendency for passenger to go straight
Force on passenger
Force on car

11. not a real force feeling due to inertia Don't get confused...
No "f" Word
not a real force
feeling due to inertia

12. What provides the centripetal force?
Tension
Gravity
Friction
Normal Force
Centripetal force is NOT a new “force”. It is simply a way of quantifying the magnitude of the force required to maintain a certain speed around a circular path of a certain radius.

13. Tension Can Yield a Centripetal Acceleration:
If the person doubles the speed of the airplane, what happens to the tension in the cable?
Doubling the speed, quadruples the force (i.e. tension) required to keep the plane in uniform circular motion.

14. Friction Can Yield a Centripetal Acceleration:

15. Car Traveling Around a Circular Track
Friction provides the centripetal acceleration

16. Centripetal Force: Question
A car travels at a constant speed around two curves. Where is the car most likely to skid? Why?
Smaller radius: larger force required to keep it in uniform circular motion.

17. Problem #1
If the radius of a circle is 1.5 m and it takes 1.3 seconds for a mass to swing around it (1 rev).
a) What is the speed of the mass? b) Find the tension if the mass is 2 kg.
s = 7.25 m/s
FT = 70.1 N

18. Problem #2
A 1200 kg car traveling at 8 m/s is turning a corner with a 9 m radius.
What is the minimum force needed to keep the car on the road?
b) Find the coefficient of static friction.
Ff = N
μ = .726

19. Problem #3
A car travels around a circular flat track with a speed of 20 m/s. The coefficient of friction between the tires and the road is Calculate the minimum radius needed to keep the car on the track.
r = m

20. Banked Curves
Why are exit ramps in highways banked?

21. Banked Curves
Q: Why exit ramps in highways are banked?

22. Banked Curves Q: Why exit ramps in highways are banked?
A: To increase the centripetal force for the higher exit speed.

23. The Normal Force Can Yield a Centripetal Acceleration:
Engineers have learned to “bank” curves so that cars can safely travel around the curve without relying on friction at all to supply the centripetal acceleration.
How many forces are
acting on the car (assuming
no friction)?

24. Banked Curves
Why exit ramps in highways are banked?
FN cosq = mg

25. Banked Curves
Why exit ramps in highways are banked?
FN cosq = mg

26. The Normal Force as a Centripetal Force:
Two: Gravity and Normal

27. The Normal Force as a Centripetal Force:

28. The Normal Force and Centripetal Acceleration:
How to bank a curve…
…so that you don’t rely on friction at all!!

29. Vertical Circular Motion

30. Vertical Circular Motion

31. Highest Point in a Vertical Circle:
ΣFy = mac
FT + mg = mv²/r
FT = mv²/r - mg
FT = m ((v²/r) - g) mg FT ac
Lowest Point ...
ΣFy = mac
FT - mg = mv²/r
FT = mv²/r + mg
FT = m ((v²/r) + g) FT mg ac

32. Critical Velocity:
Minimum velocity needed for an object to continue moving in a vertical circle. Any less velocity and the object will fall.
At this point, FT = 0, so…
ΣFy = mac
FT + mg = mv²/r
0 + mg = mv²/r
g = v2/r
rg = v2 or, vc = rg

34. The End!