1-June 12015 Conservation of Energy/Conservation of Angular Momentum

Purpose: To show that energy and angular momentum are conserved, just like regular momentum.

Theory: We can determine the angular velocity (W_1) of a mass/ruler (M_r) just before it strikes another mass/clay (M_c), with the conservation of energy formula (energy initial = energy final), then find another angular velocity at the moment of collision, with the conservation of angular momentum formula (Inertia*W_1= Inertia* W_2), and finally use another conservation of energy set up to determine the max height (h) the clay reaches, when attached to the ruler, after the collision.

Procedure: Get a meter stick and pivot it in such away that it will swing like a pendulum, weigh for mass, and determine where the pivot will be in relation to the center of mass (parallel axis theorem). Have some clay that will stick to the meter stick after collision, weigh it for mass, and set it up so the "pendulum stick" will hit the approximate center of mass of the clay when released. Use logger pro and video caption, so the max height the clay/system reaches can be accurately measured.

Apparatus

System in Motion

Measurements

*Mass of Ruler/Meter Stick (M_r): 0.077 kg

*Length of Ruler: 1.0 m

*Distance of pivot in relation to the entire Ruler: 0.01 m

*Mass of Clay (M_c): 0.0373 kg

Data collected

*Max height (h) of clay was 0.1294 m

Calculations using conservation of energy

*We will treat the "at rest" point of the ruler's swing as the zero point for gravitational potential energy.

*Because the center of mass of the meter stick is 0.5 meters, and the pivot is 0.01 meters in relation to the ruler, the center of mass will be at -0.49 m from the zero point for gravitational potential energy

*We will use the parallel axis theorem when calculating the moment of inertia for the kinetic energy portion of the problem, since the ruler isn't rotating about its center of mass and the distance from the pivot is 0.49 meters.

*The angular velocity before collision (W_1) was determined to be 5.45 rad/s

Calculations using conservation of angular momentum

*This set up works so long as the clay is struck at the center of mass, so its distance from the pivot will be 0.99 meters.

*Angular velocity after collision (W_2) was determined to be 2.208 rad/s

Calculations using conservation of energy

*We will place the zero point of potential gravitational energy at the lowest point of the swing for easier calculations.

*Max height was determined to be 0.1337 meters

*Difference percentage from actual result: 3.32%

Conclusion

*Angular momentum is conserved, just like "regular" momentum, and can be proven with the conservation of angular momentum equation (Inertia*W_1= Inertia* W_2).

*This was a very good experiment for confirming this principle

Error Analysis

*Although minor there was some error/difference from the real world result and calculated result.

*The experiment didn't account for friction due to air resistance during the motion of the system, which would influence the conservation of energy equations.