1. -Simple Pendulum -Physical Pendulum -Torsional Pendulum AP Physics C Mrs. Coyle http://article.wn.com/view/2010/08/22/Crystal_Mountain_will_feature_new_gondola_terrain_park/

2. Review: The acceleration in SHM is not constant. It is proportional to – x. To prove if a motion is SHM, you must show that the acceleration is proportional to –x. The coefficient of x is w 2. To prove if a motion is SHM, you must show that the acceleration is proportional to –x. The coefficient of x is w 2. http://www.physics.byu.edu/research/acous tics/animationsSHO.aspx

3. What if the displacement is angular, then how do you show SHM? Answer: The requirement is that the angular acceleration,   is proportional to –   Examples: Simple pendulum, physical pendulum and torsional pendulum.

4. The Simple Pendulum The motion of a simple pendulum is very close to a SHM oscillator, i f the angle is <10 o http://phys.columbia.edu/~tutorial/estimation /tut_e_2_3.html

5.  Radial:  F=T-mgcos  =0

7. Characteristics of the Simple Pendulum Angular position:  =  max cos (  t +  ) Angular frequency: Period:

8. Question 2: Does mass affect the period of the pendulum? Question 1: If a pendulum was taken to a planet where the acceleration due to gravity was four times that of g on the earth, how would the period change? See the University of Colorado Simulation Period of the Simple Pendulum

9. Physical Pendulum An object that oscillates about a fixed axis (not through its center of mass) and the object cannot be approximated as a particle. Torque  = I  For small angles sinθ=θ a=

10. Characteristics of the Physical Pendulum Since α is proportional to θ the motion is simple harmonic motion (for small angles). Angular frequency: Period:

11. Torsional Pendulum Examples: -Torsional vibrations of particles. -Torsional vibrations of bridges.

12. Torsional Pendulum Restoring torque  α  is the torsion constant of the wire

13. Characteristics of a Torsional Pendulum Angular frequency: Period: http://www.physics.ucla.edu/demoweb/dem omanual/mechanics/rotional_inertia/torsion _pendulum.html

14. Ex #39 A clock balance wheel has a period of oscillation of 0.250 s. The wheel is constructed so that its mass of 20.0 g is concentrated around a rim of radius 0.500 cm. What are: (a) The wheel’s moment of inertia and (b) The torsion constant of the attached spring? Ans: a) 5.00x10 -7 kg m 2, b) 3.16x10 -4 N m/rad