Physics problem about two rotating discs

Question

Two parallel discs are freely rotating around the same vertical axis and in the same direction. The moment of inertia of the first disc is I₁, angular velocity - ω₁. The moment of inertia of the second disc is I₂ and angular velocity - ω₂. Suddenly, the first disc falls onto the second one and they stick together. Find the angular velocity of the two discs and the change in kinetic energy of the system.

Answer 1

This is a conservation of rotational momentum question that includes a totally inelastic collision. The easiest way to do this is to calculate all the relevant values before and after the collision and then calculate the change of rotational energy.

1. Calculate the initial angular momentum for each, i*w
2. Calculate the initial angular kinetic energy for each i*w^2
3. Calculate the angular velocity of the system after the collision by setting the total angular momentum before to the total after. I1*w1+I2*w2=(I1+I2)(w3)
4. Calculate the angular kinetic energy after (I1+I2)w3^2
5. Subtract the angular kinetic energy after the collision from the total angular kinetic energy before the collision.

A pro tip for angular kinematics is to remember the many analogues to linear kinematics. If you already know the formula for linear momentum, you can figure out the formula for angular momentum. The formula for rotational kinetic energy is similar to the formula for linear kinetic energy.