1. Uniform circular motion Purpose: Determine how the linear speed of an object in uniform circular motion depends on the: 1) radius of path 2) centripetal force Procedure:horizontal spin good period value one value held constant

2. Uniform circular motion Lab analysis (on whiteboard): graph(s) relationship slope unit equation slope meaning y-intercept meaning general equation

3. Uniform circular motion (UCM) Constant linear speed (v) Constant radius

4. Uniform circular motion (UCM) Velocity is tangent to the circular path

5. Uniform circular motion (UCM) Velocity is tangent to the circular path v v v v

6. Uniform circular motion (UCM) Constant linear speed (v) Constant radius Changing direction  changing velocity  acceleration

7. Uniform circular motion (UCM) Centripetal Acceleration:  Change of velocity direction, not speed  Toward radius, perpendicular to velocity  Acceleration caused by ????????????? v v v v acac acac acac acac

8. Uniform circular motion (UCM) Centripetal Acceleration:  Change of velocity direction, not speed  Toward radius, perpendicular to velocity  Acceleration caused by unbalanced force v v v v acac acac acac acac

9. Uniform circular motion (UCM) Centripetal force:  net force along the radius that causes the circular motionF c = ΣF  points toward center  caused by other forces (F T, F g, F f, F N ) v v v v FcFc FcFc FcFc FcFc

10. Uniform circular motion (UCM) Centripetal Acceleration:  Change of velocity direction, not speed  Same relationship with net force as before Same direction a c = ΣF / m  a c = F c / m  F c = m·a c v v v v acac acac acac acac

11. Uniform circular motion (UCM) Centripetal Acceleration:  Change of velocity direction, not speed  Same relationship with net force as before Same direction a c = ΣF / m  a c = F c / m  F c = m·a c v v v v FcFc FcFc FcFc FcFc

13. Uniform circular motion (UCM) Constant linear speed (v) Constant radius Changing direction  changing velocity  acceleration Linear speed – (distance) / (time) (Circumference) / (time) v = (2·π·R) / T Period (T) – time for one complete cycle (rotation)

14. Linear speed vs. Rotational speed Rotational speed: Known as frequency – how often an event occurs f = (# rotations) / (time) unit:cycles / second = Hertz (Hz) T = (time) / (rotation) unit:seconds / cycle  (seconds) f = 1 / TT = 1 / f

15. Linear speed vs. Rotational speed Linear speed: (distance traveled) / (time) unit:m/s (mph, km/hr, etc.) Rotational speed: (# rotations) / (time) unit:cycles / second = Hertz (Hz) (rpm, rad/sec, etc.)

16. Linear speed vs. Rotational speed Merry-Go-Round example Who has: greater linear speed? AB

17. Linear speed vs. Rotational speed Merry-Go-Round example Who has: greater linear speed? A > B (more distance, same time) AB

18. Linear speed vs. Rotational speed Merry-Go-Round example Who has: greater linear speed? A > B (more distance, same time) greater rotational speed? AB

19. Linear speed vs. Rotational speed Merry-Go-Round example Who has: greater linear speed? A > B (more distance, same time) greater rotational speed? A = B (same rotations made each time) AB