1. Centrifugal and Centripetal Force

2. Vectors and Direction Key Question:
How do we describe circular motion?

3. Motion in Circles
We say an object rotates about its axis when the axis is part of the moving object.
A child revolves on a merry-go-round because he is external to the merry-go-round's axis.

4. Angular Speed
Angular speed is the rate at which an object rotates or revolves.
There are two ways to measure angular speed
number of turns per unit of time (rotations/minute)
change in angle per unit of time (deg/sec or rad/sec)

5. Angular Speed
For the purpose of angular speed, the radian is a better unit for angles.
One radian is approx degrees.
Radians are better for angular speed because a radian is a ratio of two lengths.

7. Angular Speed w = q t Angle turned (rad) Angular speed (rad/sec)
Time taken (sec)

8. Calculate angular speed
A bicycle wheel makes six turns in 2 seconds.
What is its angular speed in radians per second?
1) You are asked for the angular speed.
2) You are given turns and time.
3) There are 2π radians in one full turn. ω = θ/t
4) Solve: ω = (6 × 2π) ÷ (2 sec) = 18.8 rad/sec

9. Linear and Angular Speed
A wheel rolling along the ground has both a linear speed and an angular speed.
A point at the edge of a wheel moves one circumference in each turn of the circle.

10. Linear and Angular Speed
Radius (m)
Circumference
(m)
C = 2 P r
Distance (m)
2 P r
Speed
(m/sec)
v = d t
Time (sec)

11. Linear and Angular Speed
Radius (m)
Linear speed
(m/sec)
v = w r
Angular speed
(rad/sec)
*This formula is used in automobile speedometers based on a tire's radius.

12. Linear and Angular Speed and Displacement

13. Centripetal Force Key Question:
Why does a roller coaster stay on a track upside down on a loop?

14. Centripetal Force
We usually think of acceleration as a change in speed.
Because velocity includes both speed and direction, acceleration can also be a change in the direction of motion.

15. Centripetal Force
Any force that causes an object to move in a circle is called a centripetal force.
A centripetal force is always perpendicular to an object’s motion, toward the center of the circle.

16. Centripetal Force Fc = mv2 r Mass (kg) Linear speed (m/sec)
force (N)
Fc = mv2 r
Radius of path
(m)

18. Calculate centripetal force
A 50-kilogram passenger on an amusement park ride stands with his back against the wall of a cylindrical room with radius of 3 m.
What is the centripetal force of the wall pressing into his back when the room spins and he is moving at 6 m/sec?
1) You are asked to find the centripetal force.
2) You are given the radius, mass, and linear speed.
3) The formula that applies is Fc = mv2 ÷ r.
4) Solve: Fc = (50 kg)(6 m/sec)2 ÷ (3 m) = 600 N

19. Centripetal Acceleration
Acceleration is the rate at which an object’s velocity changes as the result of a force.
Centripetal acceleration is the acceleration of an object moving in a circle due to the centripetal force.

20. Centripetal Acceleration
Speed
(m/sec)
Centripetal
acceleration (m/sec2)
ac = v2 r
Radius of path
(m)

21. Calculate centripetal acceleration
1) You are asked for centripetal acceleration and a comparison with g (9.8 m/sec2).
2) You are given the linear speed and radius of the motion.
3) ac = v2 ÷ r
4) Solve:
ac = (10 m/sec)2 ÷ (50 m) = 2 m/sec2
The centripetal acceleration is about 20% or 1/5 that of gravity.
A motorcycle drives around a bend with a 50-meter radius at 10 m/sec.
Find the motor cycle’s centripetal acceleration and compare it with g, the acceleration of gravity.

22. Centrifugal Force
We call an object’s tendency to resist a change in its motion its inertia.
An object moving in a circle is constantly changing its direction of motion.
Although the centripetal force pushes you toward the center of the circular path...
...it seems as if there also is a force pushing you to the outside. This apparent outward force is called centrifugal force.

23. Centrifugal Force
Centrifugal force is not a true force exerted on your body.
It is simply your tendency to move in a straight line due to inertia.
This is easy to observe by twirling a small object at the end of a string.
When the string is released, the object flies off in a straight line tangent to the circle.