1. Uniform circular motion
Constant change in direction so velocity is changing.
Changing velocity implies acceleration.

2. Angular Velocity ω The rate of change of angular displacement.
Unit: Radians per second
Angles must always be in radians. 1800=π radians

3. Relationship between linear and angular speed
Let arc length = s

4. Applying Newton’s 2nd Law:
Centripetal Force
Centripetal Acceleration
The force and acceleration always point toward centre of circle.
Centripetal force is the force required to maintain uniform circular motion.

5. What provides the centripetal force?
Tension – in an object swung on a rope
Gravity – the orbiting planets
Friction – a car on a circular race track
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.

6. 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. 7

7. Tension and Centripetal Force: Vertical circle
At the top of the circle
Fc = T + mg m(v2/r) = T + mg
At the bottom of the circle Fc = T - mg m(v2/r) = T - mg
At the sides of the circle Fc = T m(v2/r) = T 8

8. Gravity Can Yield a Centripetal Acceleration:
Centripetal force = gravitational force
Keplers third law
The relationship between period, mass of the planet and radius of satellite orbit. 9

9. Friction Can Yield a Centripetal Acceleration:10

10. 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. 11

11. Banked Curves 12

12. Centripetal Force: The Roller Coaster
At the top:
net force to the centre = N + mg
m(v2/r) = N + mg
While at the bottom:
net force to the centre = N - mg
m(v2/r) = N - mg
The normal force (N) is the force the inside of a loop exerts on an object. 14