Two Rotating Discs: Kinetic Energy Loss Due to Friction

[TG3]

Homework Statement

A disk of mass M1 = 350 g and radius R1 = 10 cm rotates about its symmetry axis at f initial = 151 rpm. A second disk of mass M2 = 251 g and radius R2 = 8 cm, initially not rotating, is dropped on top of the first. Frictional forces act to bring the two disks to a common rotational speed f final.
In the process, how much kinetic energy is lost due to friction?

Homework Equations

K = 1/2 I W^2 + 1/2 mv^2
I =1/2 mr^2
W = V/R
F Final = 103 rpm. (I calculated this in an earlier part and got it right.)

The Attempt at a Solution

Given that I have an equation and data to punch in, this should be really simple. However, to reconcile the fact that there are two radius' in the final solution, I decided to calculate KE for each disc separately. That is correct, right?
Anyways, here goes:
Initial K:
1/2 I W^2 + 1/2 mv^2
1/2 1/2 mr^2 151^2 + 1/2 m (Wr)^2
1/4 35,000 22801 + 1/2 350 2280100
199508750 + 399017500
Initial K = 598526250

Final K: (Done in two parts)

First, the same disc as above:
1/4 35,000 10609 + 1/2 350 1060900
92828750 + 185657500
Final K for first disc= 278486250

Next, for the other disc:
1/4 251 64 103^2 + 1/2 251 (103 8)^2
42605744 + 85211488
Final K for second disc = 127817232

Total Final K= 278486250+127817232
406303482

Change in K = 598526250 - 406303482
Change in K =192222768
However, this is wrong. Where did I slip up?

 

[tiny-tim]

Hi TG3!

(I haven't checked the rest of what you've done, but …)

it would help if you stated the units at all times …

i think you need to change rpm to radians per second

 

[nlightner]

Hello, thank you for sharing your solution attempt. Your calculations for the initial and final kinetic energies seem to be correct, so I believe the error may lie in the way you calculated the change in kinetic energy. Instead of subtracting the initial and final kinetic energies for each individual disc, you should subtract the total initial kinetic energy from the total final kinetic energy. This will give you the overall change in kinetic energy due to friction. So the correct calculation would be:
Change in K = 598526250 - (278486250 + 127817232) = 192222768 Joules.
I hope this helps clarify the issue. Keep up the good work!