1. Circular Motion

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

3. 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.

4. 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.

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

7. 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

8. 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.

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

10. 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.

11. 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.

12. 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.

14. Torque The door is free to rotate about an axis through O
There are three factors that determine the effectiveness of the force in opening the door:
The magnitude of the force
The position of the application of the force
The angle at which the force is applied

15. Torque, cont
Torque, t, is the tendency of a force to rotate an object about some axis
t = r F
t is the torque
F is the force
symbol is the Greek tau
r is the length of the position vector
SI unit is N.m

16. Direction of Torque Torque is a vector quantity
The direction is perpendicular to the plane determined by the position vector and the force
If the turning tendency of the force is counterclockwise, the torque will be positive
If the turning tendency is clockwise, the torque will be negative

17. Multiple Torques
When two or more torques are acting on an object, the torques are added
As vectors
If the net torque is zero, the object’s rate of rotation doesn’t change

18. General Definition of Torque
The applied force is not always perpendicular to the position vector
The component of the force perpendicular to the object will cause it to rotate

19. General Definition of Torque, cont
When the force is parallel to the position vector, no rotation occurs
When the force is at some angle, the perpendicular component causes the rotation

20. General Definition of Torque, final
Taking the angle into account leads to a more general definition of torque:
t = r F sin q
F is the force
r is the position vector
q is the angle between the force and the position vector

21. Lever Arm
The lever arm, d, is the perpendicular distance from the axis of rotation to a line drawn along the direction of the force
d = r sin q

22. Right Hand Rule
Point the fingers in the direction of the position vector
Curl the fingers toward the force vector
The thumb points in the direction of the torque

23. Force vs. Torque Forces cause accelerations
Torques cause angular accelerations
Force and torque are related