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

5. Quantifying Acceleration: Magnitude
Centripetal Acceleration

6. 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.

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

8. Direction of Centripetal Force, Acceleration and Velocity

9. What if velocity decreases?

10. What if mass decreases?

11. What if radius decreases?

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. Relationship Between Variables of Uniform Circular Motion
Suppose two identical objects go around in horizontal circles of identical diameter but one object goes around the circle twice as fast as the other. The force required to keep the faster object on the circular path is
the same as
one fourth of
half of
twice
four times
the force required to keep the slower object on the path.
The answer is E. As the velocity increases the centripetal force required to maintain the circle increases as the square of the speed.

14. Relationship Between Variables of Uniform Circular Motion
Suppose two identical objects go around in horizontal circles with the same speed. The diameter of one circle is half of the diameter of the other. The force required to keep the object on the smaller circular path is
the same as
one fourth of
half of
twice
four times
the force required to keep the object on the larger path.
The answer is D. The centripetal force needed to maintain the circular motion of an object is inversely proportional to the radius of the circle. Everybody knows that it is harder to navigate a sharp turn than a wide turn.

15. Relationship Between Variables of Uniform Circular Motion
Suppose two identical objects go around in horizontal circles of identical diameter and speed but one object has twice the mass of the other. The force required to keep the more massive object on the circular path is
the same as
one fourth of
half of
twice
four times
Answer: D.The mass is directly proportional to centripetal force.

16. 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.

17. Friction Can Yield a Centripetal Acceleration:

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

19. page 166
65. Friction provides the force needed for a car
to travel around a flat, circular race track.
What is the maximum speed at which a car
can safely travel if the radius of the track is
80.0 m and the coefficient of friction is 0.40?

20. 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.

21. Why does centrifugal force not actually exist?
Centrifugal force is believed by some to be
an outward force that exists when an object
is in uniform circular motion. However, if
the centripetal force that keeps an object in
uniform circular motion is suddenly
removed, the object does not fly outward
away from the center of the circle. It moves
along a line tangential to the circle. Thus,
there is no centrifugal force.

22. Questions solving:
17 & 18 page 156
Q 36 & 37page 164
Q 61 ,62 ,64 page 166

23. Vertical Circular Motion

24. 66.Page 166 (vertical circular motion)
A carnival clown rides a motorcycle down
a ramp and around a vertical loop. If the
loop has a radius of 18 m, what is the
slowest speed the rider can have at the top
of the loop to avoid falling? Hint: At this
slowest speed, the track exerts no force on the
motorcycle at the top of the loop.

25. 67. A 75-kg pilot flies a plane in a loop as shown in Figure 6-15
67. A 75-kg pilot flies a plane in a loop as shown in Figure At the top of the loop, when the plane is completely upside-down for an
instant, the pilot hangs freely in the seat
and does not push against the seat belt. The
airspeed indicator reads 120 m/s. What is
the radius of the plane’s loop?

26. 78. A 1.13-kg ball is swung vertically from a
0.50-m cord in uniform circular motion
at a speed of 2.4 m/s. What is the tension in
the cord at the bottom of the ball’s motion?

27. Circular Motion Concepts on line Quiz
Circular Motion Numerical on line Quiz:

28. The End!