Rotating Disks - How to calculate final KE?

[taveuni]

Hi, I have worked through this problem for so long that I cannot see how I could be getting it wrong. I feel like I am doing it correctly, but I don't get the right answer.

QUESTION
A disk of mass M1 = 350 g and radius R1 = 10 cm rotates about its symmetry axis at finitial = 154 rpm. A second disk of mass M2 = 260 g and radius R2 = 7 cm, initially not rotating, is dropped on top of the first. Frictional forces act to bring the two disks to a common rotational speed ffinal.

a) What is ffinal? Please give your answer in units of rpm, but do not enter the units.
ff= 112.9 rpm​

b) In the process, how much kinetic energy is lost due to friction?
|KElost| = ? J​

MY THOUGHTS:
I figure that the change in KE is equal to .5*(Ii*wi^2)-.5*(If*wf^2). KEi is easily calculated and is 0.22756 J.

Is it fair to assume that the If in KEf is the sum of the I's for both disks, because they are now spinning together? I did that, came up with I(sum)=0.002387, which gives a If of 0.11683.

KEi - KEf = change in KE
0.22756-0.11683 = 0.06073 - which is wrong.

Should I be incorporating translational KE into this? I tried that and also go the wrong answer.

Thank you for your insight.

 

[Hootenanny]

KEi - KEf = change in KE
0.22756-0.11683 = 0.06073 - which is wrong.

Here is your problem. $0.22756-0.11683\neq0.06073$. Looks like you pushed the wrong buttons on your calculator

 

[kyle8921]

RESPONSE:
It appears that you are on the right track with your approach to calculating the final KE. However, there are a few things to consider in this problem that may be contributing to your incorrect answer.

Firstly, when the second disk is dropped on top of the first, it will not only add to the moment of inertia of the system, but also add to the angular velocity. This means that the final angular velocity will not be the same as the initial angular velocity of the first disk (154 rpm). Instead, it will be a weighted average of the two angular velocities, taking into account the masses and radii of both disks.

Secondly, it is important to remember that the kinetic energy lost due to friction will be equal to the difference between the initial and final KE, not the difference between the initial and final angular velocities. This means that you will need to use the final KE in your calculation, which will include the contribution from both disks.

Finally, it is not necessary to incorporate translational KE into this problem, as the disks are rotating about their symmetry axis and there is no translational motion involved.

In summary, to correctly calculate the final KE, you will need to consider the weighted average of the two angular velocities, use the final KE in your calculation, and remember to take into account the contributions from both disks. I hope this helps and good luck with your calculations!