# Conservation of angular momentum and rotational kinetic energy

Saptarshi Sarkar
Homework Statement:
A thin uniform disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity ##\omega##. Another disk of same dimensions but mass M/4 is placed on the first disk coaxially. What is the angular speed of the system is now
Relevant Equations:
##K.E. = \frac 12I\omega^2##
##L= I\omega##
I first tried to get the solution by conserving the rotational kinetic energy and got ##\omega'=\frac2{\sqrt5} \omega##.

But, it was not the correct answer. Next I tried by conserving the angular momentum and got ##\omega'=\frac 45 \omega##, which is the correct answer.

Why is the rotational kinetic energy not conserved here? Where is the energy being used up?

Gold Member
Energy used up calculated as
$$\frac{1}{10}I\omega^2$$
is used up when two disks was getting the same angular speed in most cases by friction between the surfaces.

Delta2 and Saptarshi Sarkar