1. Circular Motion

2. Uniform Circular Motion Motion of an object at constant speed along a circular path

3. Velocity is changing r1r1 r2r2 Radius – Measured in meters v1v1 v2v2 If Velocity is changing, then it must be accelerating!

4. Velocity Velocity vector is always tangent to the curve of the circle in the direction of the motion (Imagine what would happen if you let go, where would the object go?)

5. Acceleration Equation: a c = v 2 /r a c = centripetal acceleration (m/s 2 ) v = velocity (m/s) r = radius (m)

6. Newton’s Second Law When an object undergoes a constant acceleration, there must be a constant force acting upon it. Centripetal Force F=ma a c =v 2 /rv 2 /r

7. Centripetal Centripetal means center seeking. So centripetal force and acceleration are always center seeking FcFc

8. Recap a c = v 2 /r F c = mv 2 / r Force and Acceleration are pointing towards the center Velocity is tangent to the curve

9. CAREFUL!!! Common Misconception CentriPETAL – Towards Center CentriFUGAL – Away from center - Doesn’t actually “exist.” - It is used to describe the apparent outward force that you feel. - This force is because of Newton’s Third Law: For every force there is an equal and opposite force.

10. Example An object with mass of 5.0 kg moves in a circular path of radius.50 m at a speed of 10 m/s a) Calculate the centripetal acceleration b) Calculate the centripetal force Answer: a) 2.0 x 10 2 m/s b) 1.0 x 10 3 N

11. On Your Own A 10 kg object moves in a circular path of radius 9 m with a velocity of 4 m/s. a) Find the centripetal acceleration of the object b) Find the centripetal force on the object

12. 1. A 5 kg object moves in a circular path of radius 2 m with a velocity of 6 m/s. a) Find the centripetal acceleration of the object b) Find the centripetal force on the object 2. Draw an object going around in a circle. Label the velocity vector, force vector and acceleration vector (Which way will they be pointing?) HAND IN

13. Linear Speed – Speed in a straight line, distance over time Tangential Speed – Speed in a circle, velocity is tangent to the curve Rotational Speed - # of Rotations per amount of time