AP Physics C Mechanics 2017 FRQ #3, Conservation of Energy & Rotation

[Lara-yrw]

I was wondering if you would explain why the following method of using conservation of ME would NOT work for part (b):
k1+u1=kf+uf --> 2.5+mg(0.75)=k[trans, f]+k[rot, f]+ 0 --> 6.25=0.5mr^2w^2 + 0.5*I*w^2 --> w= 40.8 rad/s. I understand the method that you used in the video, but this is the one I went with, and can't figure out why it is incorrect.

[mastering_science]

Your question is a good one. We set the height for the table =0 for the original calculation of 1-->2, which will give us the kinetic energy at 2. Then we later do a calculation (for part c) that does include the new h=0 for the floor as we look at 2-->3. We can do that. We don't have to have the same h = 0 reference for every part of the problem, as long as we don't use different zero values within one set of calculations. In other words we can treat 1-->2 almost as a separate problem from 2--> 3. It's just that solutions for 1-->2 will feed into 2-->3.

[mastering_science]

We used the height difference in a solving for a basic conservation of energy problem going from 1 --> 2. It was implied in part b (and in part c) that the gravitational potential energy at the floor was zero, looking at 2 --> 3. Having said that, in hindsight it may have been more helpful if I would have written that the potential energy at the floor was zero. The key for understanding part b is that while the total kinetic energy of the cylinder would change going from 2 --> 3 as a normal conservation of energy problem, it's rotational kinetic energy would be exactly the same at 2 and 3. This is because nothing is turning (applying a torque) on the cylinder while it's in the air. So if you solve for the angular velocity at 2, you've also solved for it at 3. The question in b has to do with the angular velocity of how fast the object is spinning at 3, not it's total kinetic energy at b (which would have to take into account the drop from 2 --> 3, and if that was the case you'd be right, I'd need to add in a term for the potential energy drop from 2 --> 3). Part c is asking about total kinetic energy, which needs to take into account the drop in potential energy from the table to the floor. Good question by the way, Begum.

[ronitkapoor]

Why is the gravitational potential energy neglected at the bottom when calculating the angular velocity. Your solution in part a denotes that the gpe=0 line is at the table, and if that was the case then there would be negative potential energy included in your conservation statement.
\\