PHYS4A/ Fall 2014; Angular Momentum

Purpose: Using angular momentum and the concept of conservation of momentum, we will predict how high a ruler will swing after an inelastic collision with a piece of putty.

For this experiment, we split the problem into two parts in order to show that momentum is conserved in a rotational collision. To do this, we had set up a ruler and putty scenario where the ruler would start at an angle and be released from rest so that it would hit a piece of putty resulting in an inelastic collision. The goal would then be to calculate the momentum and show that the momentum was conserved throughout the process.

Ruler and putty set-up

The above set-up was created with a camera set across from the ruler centered on the location that the putty ended up at the peak of the rotation. Once we were set-up, the ruler was lifted and released from rest to hit the putty and pick it up. The camera was used to record a video of the motion and loggerpro was used to analyze the data. 

LoggerPro's view of the collision and plotting the points frame by frame of the path of the putty.

When analyzing the video, we had to put a point on the path of the putty, frame by frame. Once all of the points were plotted, we were able to see a fairly smooth curve along a circle. Once the video was finished analyzing, we calculated a theoretical final height for the putty by splitting the experiment into two intervals. For the first interval, we used conservation of energy starting at the initial point at rest to just before the ruler hit the putty.

Total Energy = Potential Energy = Rotational Kinetic Energy

mgh = (1/2)Iw^2

By using conservation of energy we were able to calculate the angular velocity just before the ruler hits the putty. This angular velocity was then used to calculate for the angular velocity just after the collision using conservation of rotational momentum. Initially, the rule was moving at some angular velocity. Then, once it makes contact, its mass changes and it has a new angular velocity. Since the collision was inelastic, energy was not conserved but momentum was. This new omega was then used in the next part of the calculations to finally come up with final height.

All the messy work in our calculations (which Prof. Wolf called beautiful)

Final part of the calculations where we find the height.

The last part to find the height was by using conservation of energy once again. Using the angular velocity of the moment right after collision as the initial speed, we were able to compare that to when the ruler and putty stopped at the end of the path. By using conservation of energy again, this time starting with rotational kinetic energy and ending with gravitational potential, we were able to calculate the height of the putty to be 0.303m.

Knowing this height, we went back to loggerpro and set an axis at the origin of the collision, then using the analysis data it was able to give us a final height. Since both the calculations and loggerpro were both using the same axis, the values could be directly compared to each other. From loggerpro, we got a value of 0.2325m where the theoretical was 0.303m. The experimental value being lower does make sense due to frictional forces such as air drag or friction at the pivot. Therefore, we were able to prove that momentum is conserved in a rotational collision.