1. Other 2D Motion Periodic Motion: SHM and UCM what’s with all these letters?

2. Portoflio Problems  A car is getting off the interstate. The ramp is a circle, and the posted speed limit is 45 mph. If the centripetal accleration should be.3 g, what is the minimum radius the ramp should be?  A pendulum of length 1 m is brough to planet X. The period of this simple pendulum is found to be 1.5 minutes. What is the gravity on planet X?

3. College Prep Portfolio  A car is getting off the interstate where the speed limit is 65 mph. If the centripetal acceleration should.3 g and the radius of the ramp is 120 feet, how far should be allowed for the deccleration lane?

4. Periodic Motion (CH 7)   type of motion in which a body is repeatedly moving over the same path in equal intervals of time  Examples:  spring  pendulum  merry-go-round??????  UCM and SHM

5. Uniform Circular Motion  UCM  the motion of an object at constant spd, NOT velocity, along a curved path of fixed radius  is the particle accelerating??

6. UCM ctd.  Period  time required for one complete revolution (units of time)  T = 2*pi*r/|v|  where pi = 3.14....  r = radius of circle  v = velocity of object  Why 2*pi*r?  (Dist around circle)  Frequency  inverse of period  units of Hertz  inverse sec  Angular velocity (  )  how fast something rotates

7. More UCM  Displacement Vectors  Same magnitude  directed from center out  Velocity Vectors 1.same magnitude (same speed, same length) 2.diff directions, tangent to circle and perpendicular to displacement vector  Acceleration Vectors  centripetal acceleration  “center seeking”  directed in toward center  always opposite of displacement  a c = v 2 /r Also: a c =4  2 r/T 2

8. Simple Harmonic Motion  Gotta keep those lovin’ good vibrations are happening with her  SHM  type of motion in which a particle’s acceleration is proportional to its displacement from its equilibrium position and is always directed toward equilibrium  examples  vib tuning fork  mass on string  simple pendulum

9. SHM Properties  equlibrium  midpoint of path  displacement  dist from equil  what is this for UCM?  radius  amplitude  max displacement  period  time for 1 complete vibration  frequency  # of vibrations per unit time Before it starts: x = 0 v = 0 a = 0 Start it off! x = 0 (equil) v = max a = 0 x = amplitude v = 0 a = max x =ampl v =0 a = max a shm = 4  2 x/T 2

10. Pendulum  Tic Toc, Tic Toc,  def = an object mounted in such a way that it can swing back and forth about an axis  Properties:  pd. is indpt of mass  pd is indpt of amplitude  these imply that the arc is small (less than 15 o )  pd  sqr(length)  pd  1/sqr(g) T = 2  *sqrt(l/g)

11. Pendulum In Motion x = amp v = 0 a = max x = amp v =0 a =max x = 0 v = max a = 0

12. Book Problems  UCM  pg. 145  #10 a, 11 a (ignore references to force)  pg. 151 RC  #4  pg 152 Problems  #13 a, #14 a, #16 a,b,d, #17 a, #18 a,b, #19 a  SHM  pg. 149  #13,14  pg. 151 RC  #9, #10, #12 (ignore force)  pg. 152 AC  #10,11  pg. 152 Problems  #21,22