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# Periodic Motion

Periodic Motion. Torque. Define Torque A measure of a force’s ability to twist or rotate an object. (The result of a force when tends to produce rotation.) Equation = r F Qualitative Understanding Investigate the opening/closing of doors and lifting/supporting of objects. Example #1.

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## Periodic Motion

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1. Periodic Motion

2. Torque • Define Torque • A measure of a force’s ability to twist or rotate an object. (The result of a force when tends to produce rotation.) • Equation • = r F Qualitative Understanding Investigate the opening/closing of doors and lifting/supporting of objects.

3. Example #1 Two friends are playing on a seesaw. The heavier friend, 55 kg, sits 1.75 m from the fulcrum (pivot point, or axis of rotation). How far from the fulcrum must the lighter friend, 35 kg site to balance the seesaw.

4. UCM PreLab • The objective of the UCM Lab is to investigate uniform circular motion. • Review the relationship between frequency and period. • Practice maintaining a uniform horizontal circle with the string free to move.

5. UCM PreLab • Students should review the following skills: • Graphing Skills Sheet • Linearization Skills Sheet • Conclusion Skills Sheet

6. UCM Post Lab Variable Relationships Examine position, displacement, velocity acceleration and net force for an object in UCM. Draw and label the quantities below on the sketch below and complete chart with yes, or no.

7. UCM Post Lab Graph Analysis Make additional graphs of v vs r And a second graph of v2 vs r. If either graph is linear, find it’s slope. V2 r

8. UCM Post Lab What was the direction of the acceleration of the stopper? What was the direction of the velocity? Draw velocity and acceleration vectors on the picture below. Draw a Free Body Diagram (FBD) for the forces acting on the stopper. What is the net force acting on the stopper?

9. UCM Post Lab Free-Body Diagram Draw FBDs for m1 and m2. What relationship exists between the forces of the hanging mass and the centripetal force on the stopper?

10. Example #2 A mass, 0.1 kg, is whirled around by a string of length 0.75 m.  It makes 20 revolutions in 10 seconds. What is the frequency? What is the period?

11. Example #2 A mass, 0.1 kg, is whirled around by a string of length 0.75 m.  It makes 20 revolutions in 10 seconds. What is the speed?

12. Example #2 A mass, 0.1 kg, is whirled around by a string of length 0.75 m.  It makes 20 revolutions in 10 seconds. What is the centripetal acceleration?

13. Example #2 A mass, 0.1 kg, is whirled around by a string of length 0.75 m.  It makes 20 revolutions in 10 seconds. What is the tension in the string?

14. Pendulum PreLab: Lab Assessment • What relationship is being researched? • What are the constraints? • The objective of the PendulumLab is to investigate pendulummotion without any teacher assistance. No prelab information will be given other than safety concerns. • Students’ questions will NOT be answered. • Remind students for review the following skills: • Graphing Skills Sheet • Linearization Skills Sheet • Conclusion Skills Sheet

15. Pendulum Post Lab What affects the period of a pendulum? Graph Analysis Derive period equation from lab data and variables. Manipulate derived period equation to include correct math and physics constants.

16. Mass on a Spring Kinematics of an Oscillating Vertical Mass Investigate the graphs of motion for an object in SHM (motion detector). What patterns can be found between the position, velocity and acceleration for the oscillating mass? Complete the charts and graphs of motions in the lecture notes.

17. Mass on a Spring Dynamics of a Oscillating Vertical Mass Draw FBDs at equilibrium, maximum amplitude and points in between for an object in SHM. Identify positions of maximum and minimum: displacement, velocity, acceleration and net force. Let the dashed line represent the equilibrium position. Complete the FBDs in the lecture notes.

18. Mass on a Spring +A x time T -A

19. Mass on a Spring +Vmax v time T -Vmax

20. Mass on a Spring +amax a time T -amax

21. Mass on a Spring Dynamics of a Oscillating Vertical Mass Draw FBDs at equilibrium, amplitude and points in between for an object in SHM. Identify positions of maximum and minimum: displacement, velocity, acceleration and net force. Let the dashed line represent the equilibrium position. ------------------------------------------------------------------------------------

22. Example #7 A spiral staircase winds up to the top of a tower in an old castle.  To measure the height of the tower, a rope is attached to the top of the tower.  However, nothing is available to measure the length of the rope. So, at the bottom a small object is attached so as to form a simple pendulum that just clears the floor. The period of the pendulum is 9.2 seconds. What is the height of the tower?

23. Example #8 From the period of a pendulum set up in the classroom, determine the acceleration due to gravity in your classroom.

24. Example #9 A pendulum clock can be approximated as a simple pendulum of length 1.00 m and keeps accurate time at a location where g = 9.83 m/s^2.  In a location where g = 9.78 m/s^2, what must be the new length such that the clock keeps accurate time? (So that the period remains the same).

25. SHM and UCM Connection SHM is a one-dimensional projection of two-dimensional UCM

26. SHM and UCM Comparison What effect do the follow variables have on the period of oscillation for a mass on a spring and a pendulum?

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