1. Circular Motion

2. PhET Lady Bug Motion

3. Think about this Click “Show Both” at the top, and “Circular” at the bottom Watch the following and comment: Which color vector represents velocity, and which represents acceleration? Velocity = Green or Blue Acceleration = Green or Blue

4. Velocity vectors differ in length because of speed

6. Speed affects both velocity vector and acceleration vector length

7. Forces involved in Circular Motion

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

9. Uniform Circular Motion Uniform circular motion is the motion of an object rotating or revolving at a constant speed. Although its speed is constant, an object moving in a circle is accelerating, because the direction of its velocity vector continually changes.

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

11. 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?)

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

13. Newton’s Second Law Objects accelerate in the direction of the net force. Centripetal Force- is the net force that accelerates objects in a circular path ∑=ma a c =v 2 /r F

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

15. Recap a c = v 2 /r F c = m(v 2 / r) Force and Acceleration are pointing towards the center Velocity is tangent to the curve

16. 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.

17. FcFc The object “wants” to go in this direction. This imaginary pull. If the F c is removed the object will travel in a straight line path not because of a force but because of lack of force, we call this inertia

18. 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 2 b) 1.0 x 10 3 N

19. On Your Own 1. 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

20. 2. 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 3. 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

21. Rotational Motion

22. Rotating vs Revolving Objects Rotating objects spin The axis of rotation is inside the object Revolving objects move in circles where the axis of rotation is outside the object Example: The Earth rotates about its own axis and revolves around the sun

23. Frequency Frequency, f, describes how many times an object repeats its motion in a given time interval. It is measured in cycles/seconds, called Hertz (Hz). Example: A wheel that rotates 7 times every second has a frequency of 7 Hz.

24. Period Period,T,describes the time it takes for a motion to repeat itself. Period is measured in seconds. A period is the reciprocal of frequency. T= 1/f Example: A wheel that rotates 5 times every second has a period of 0.2sec.