31-May-2017: Conservation of Energy/Conservation of angular momentum

We learned the conservation of linear momentum before, which is when the collision happens the momentum always conserved. Also, when the object did not have any transformation or any other force on it, the energy will also conserve. So will it be similar to the object when it is rotating? Today, we set up a lab to study on it.

Purpose

Verify the conservation of energy and angular momentum.

Plan

We release a meter stick, pivoted at or near one end, from a horizontal position.
When the meter stick reaches the bottom of its swing it collides inelastically with a blob of clay. The meter stick and clay continue to rotate together to some final position.

Then, measure the appropriate masses, etc.
Make a prediction for how high the clay stick combination should rise by the following functions.

Then capture the experiment on video and compare your actual results with your predictions.
If the energy and angular momentum are conserved, it should give us the same result as what we calculated by the theorem.

Set up & data

We set up the apparatus as follows. (Notice: there are some nails at the end of the rule to make sure that the clay would stick with it, and the pivot point is at the 10cm.)

Measure the weight of ruler and the clay. We got the rule is 97.39g, and the clay is 19.89g. 

Use the iPhone's slow motion camera to collect the video when the ruler started to drop down till it reached the highest point. 

Next, use the Logger Pro to get the data. 

And we get it would reach 37cm. 

Analyze

Through the functions 

We predicted the height of the clay should raise 0.394 m 

Compare with the actual value, 

(0.394 - 9.3743)/0.394 ≈ 5%

which is pretty close. 

Thus, we said the energy and angular momentum is conserved during the similar process as linear. 

Conclusion

This lab verified that the conservation of energy and angular momentum as it only give us the 5% difference in the result. Due to some measure uncertainty (like the capture of video might be not so exact, the measure of the ruler's and the clay's weight), there is some acceptable error on it. Moreover, like the linear conservation, there might be some friction force on the ruler, and the inertia may not be so accurate since the ruler is not uniformity. 

Overall, this lab is good enough to proof that the energu and angular momentum are conserved during each part of collision.