Lab 19: May 31, 2017: Conservation of Energy and Angular Momentum

Lab 19: Conservation of Energy and Angular Momentum 

Amy, Chris, and John

May 31,2017

In today's lab we were testing the conservation of energy and the angular momentum bu making a ruler collide with a piece of clay on the ground. 

Theory: Due to the absence of external forces, angular momentum is conserved alike linear momentum. When we assume there are no external forces, these quantities would actually equal because the angular momentum before the collision is equal after the collision. 

The inertia of our object, thought of as a system of objects where the total inertia is the sum of all individual inertias about the axis of rotation of a system. Which in our case is I=ML^2. For this inertia L is the distance away from the axis of rotation. For our lab, we tested to see if the angular momentum is conserved, before and after the collision. in order to find our angular velocity within our momentum formula, we assume there is a conservation of energy. Should we assume there is a conservation of energy then the height our clay would reach in our system would be calculated by; 

Using the value of omega we calculated we are able to solve for the omega after collision with the conservation of angular momentum. Because our axis of rotation for the meter stick is not exactly placed at the end, we used the parallel axis theorem to find the new moment of inertia about the new axis. Applying this to the conservation of momentum would give us omega final. 

the omega final we calculated can be used in our conservation of energy equation. Initial energy will be the kinetic rotational energy and this will transfer to gravitational potential. The only unknown for the equation we used is theta so we can isolate and solve for it. 

 This inverse gives us the angle for which the meter stick travels up after sticking with the clay. By using this angle, we can now find the height our clay reached. Isolating the distance the clay is away from the axis of rotation and the (1-cos(theta)) portion. 

Apparatus and Procedure: We set up  our apparatus using a stand attached to a pivot point and put the pin through the hole previously drilled in the meter stick. We recorded a slow motion video of the collision at 240 frames per second of the meter stick colliding with the clay. We then uploaded the video to Logger Pro, having the video on Logger Pro allowed us to analyze how high our meter stick went by setting up our axis. As we performed the experiment we were not surprised that the conservation of momentum really holds in this experiment. Knowing the quantities of the mass of the meter stick. mass of clay, and distance from the axis from the meter stick and clay we were able to test the theorem. 

Data: The point of the meter stick that the axis of rotation went through was at the 2 centimeter mark. 

	r distance from axis (m)	Mass (kg)
Meter stick	0.48	0.02357
Clay	0.98	0.1444

The video capture as well as the height reading of the clay blob.

The height recorded was 0.4310 m.

Calculated Data:

The parallel axis theorem for the meter stick:

The conservation of energy to find omega initial:

and for omega final calculations, we need the total system inertia after collision:

Now plugging in values to our formula for deriving the angle theta that the ruler rises:

and to find the max height of the clay using the angle above:

Conclusion: 

Calculating for percent error between our experimental value and theoretical gives us:

This value is ranked among the higher end of the spectrum. ideally we want to get below 5%. Which is a rather large margin of error. We could have multiple sources of error in this experiment. For one, we neglect the friction at the axis of rotation where our meter stick swung to hit the clay. Our theoretical values was higher than our experimental, most likely due to error in calculations and the lack of accuracy that our theoretical value would not account for. The video analysis we did for Logger Pro could have been slightly tilted for our axis in our video. Recording the video from a random point of view could also affect our measurements on Logger Pro as well. We also made assumptions like treating the clay as a point mass and energy being conserved when it may have not been. Because of the measurements made were such estimates that did not take much into account may also have affected our calculated values.