1. PRINCIPLES OF PHYSICS Circular Motion

2. When an object moves in a circle its path is described by: Radius (r) – distance from the center to the perimeter (meters) Circumference (C) – perimeter of circle (2πr) (meters) Period (T) – time to go around the circle once (seconds) r

3. Rotational Speed (scalar quantity) number of times around the circle per unit time (rot/s) Linear Speed (v) Distance per unit time Rotational Speed vs Linear Speed

4. Example: An object is moving around a circle of radius 5m. It completes 5 rotations every second. How fast is it going?

5. Assume linear speed (what the speedometer in your car would read) is not changing during motion in a circle Speed is constant Direction is changing If velocity is changing then the object is accelerating If the object is accelerating then an unbalanced force must be acting on it Centripetal Force Changing Velocity

6. Remember: Newton’s 1 st Law → objects in motion stay in motion in straight lines unless a force is acting So, A force must be acting on an object if it is travelling in along a circular path Special name – centripetal force (F c ) (centripetal = center seeking) **No such thing at centrifugal or centrifical force Centripetal Force

7. To move in circles the direction of the force is always changing, but always directed toward the center of the circular path. F c, a c v Centripetal Force

8. Centripetal force is another name for any force that causes an object to move in circles Therefore, Any type of force can be a centripetal force Example: friction keeps cars moving around circular ramps when entering or exiting the highway. Centripetal Force

9. We know: F = ma, so F c = ma c a c = centripetal acceleration = v 2 /r so, F c = ma c = mv 2 /r Calculating Centripetal Force F c = ma c a c = v 2 /rF c = mv 2 /r

10. Example 1: A 1.0 kg ball attached to a string 0.50 m long is swung in a circle. Its speed along the circular path is 6.0 m/s. What are a c and F c ? m = 1 kg r = 0.5 m v = 6 m/s a c = v 2 /r = (6m/s) 2 /0.5 m = 72 m/s 2 F c = ma c = 1 kg (72 m/s 2 ) = 72 N

11. Example 2: Suppose a 5 kg object is being held in a circular path of radius 20 m with a force of 400 N. What is the speed of the object? F c = mv 2 r 400 = 5v 2 20 400(20) = 5v 2 5 5 1600 = v 2 v = 40 m/s m = 5 kg r = 20 m F = 400 N