1. Circular Motion

2. Constant speed but accelerating??
Velocity is a vector. The speed (magnitude) may remain the same but the direction can change.
Any change in velocity is caused by an acceleration.
Circular path changes direction of velocity.
Moving at a constant speed in a circle is called uniform circular motion (UCM).

3. v1
position
vector r1 v2 r2

4. Centripetal Acceleration
Centripetal acceleration is the acceleration of an object in UCM.
This acceleration always points to the middle of the circle.
ac = v2 r
Units are still m/s2

5. Finding v
v = d/t
t is equal to the period (T): time for one full revolution.
d is the distance around the circle
Circumference equals 2πr
So v = 2πr T

6. Centripetal Force
If an object is accelerating, there must be a net force in the direction of the acceleration, toward the center of the circle.
Newton’s 2nd Law says F=ma
Fc = mac or
Fc = mv2 r
Animation

7. Putting centripetal force to work.
When a car travels around a corner the net force is the friction between the car and tires. This changes the direction of the cars velocity.
If the road is icy the centripetal force decreases and the velocity will not change direction. The car will move straight off the road.
Animation

8. Where Else Do We See This?
Discus
Hammer Throw
Ride

9. The Fake Force
When a person driving slams on the brakes you move forward, the force and acceleration act in the opposite direction you move. Inertia makes you move forward.
Centrifugal force which makes you feel like you are being pushed against the outside of a circular moving object is just inertia. It is a nonexistent force.

10. Practice
A .3kg ball on a 1.2m string is traveling in a horizontal plane at 6.1m/s.
Find the centripetal acceleration.
Find the centripetal force.

11. One More
A car with a mass of 1500kg travels around a curve with a radius of 45m. The car is traveling at a speed of 20m/s.
Find the centripetal acceleration of the car
Find the centripetal force acting on the car
Find the force of friction acting on the car.