Help with physics please?

Question

Help with physics please?
I have no idea what to do here, any explanation would be great.

In the figure the large mass disk has mass 2 kg radius 0.2m and initial angular velocity 50 rad/sec and the small disk has mass 4kg radius 0.1m and initial angular velocity 200 rad/sec (about 1900 rpm). A) find the common final angular velocity after the disks are pushed into contact. B) Is kinetic energy conserved during this process.

Answer 1

Hmm... I believe you would approach this problem the same way you approached collisions earlier on in your physics career. Recall that in any collision, momentum is conserved.

In this case, angular momentum should be conserved. Now, I can't see the figure they're talking about, but I assume the axes of the two spinning disks are approaching each other, so that the faces of the two spinning disks will come into contact.

Just as we expressed momentum: p=mv, we express angular momentum: L=Iω. (You'll find that when dealing with angles, I and ω typically replace m and v respectively.)

The moment of inertia (I) of a disk is I=½*m*r². Likewise, the moment of inertia of the final system, with one disk sitting on top of the other disk, will be the sum of the moments of each disk, or I_final = ½*m_1*r_1² + ½*m_2*r_2²
(Generally speaking, I_total = Σ½*m_i*r_i²)

Since you are given the initial angular velocities, you can then solve for the initial angular momentum of each disk, and then since angular momentum is conserved, solve for the final angular momentum of the combined system (where the one disk sits on top of the other disk), from which you can solve final angular velocity. If the two disks are spinning at the same "rate" then they share the angular velocity, since angular velocity is independent of the radius of the respective disk.

Then, you can solve for the initial kinetic energies and the final kinetic energy to determine whether kinetic energy was conserved or not. Recall that for a rotational system, kinetic_energy=½*I*ω². (Again note that I and ω have replaced m and v respectively.)