Homework Help: Calculating Kinetic Energy with Rotational Motion

1. Oct 13, 2011

embudini

1. The problem statement, all variables and given/known data
A student sits at rest on a piano stool that can rotate without friction. The moment of inertia of the student-stool system is 3.6 kg·m2. A second student tosses a 1.7 kg mass with a speed of 3.0 m/s to the student on the stool, who catches it at a distance of 0.38 m from the axis of rotation. The final angular speed is 0.504 rad/s.
(a) Does the kinetic energy of the mass-student-stool system increase, decrease, or stay the same as the mass is caught?

(b) Calculate the initial and final kinetic energy of the system.

2. Relevant equations
W=Kf-Ki
ω=v/r

3. The attempt at a solution

2. Oct 13, 2011

cepheid

Staff Emeritus
Welcome to PF embudini!

How does the moment of inertia of the system change after the person on the stool catches the mass?

How does the rotational kinetic energy of a system depend on its moment of inertia and on its angular velocity ω?

3. Oct 13, 2011

embudini

The moment of inertia would increase because the system has a greater mass.

The kinetic energy is .5mv^2+.5Iω^2, the combination of its linear and rotational kinetic energies. But I don't know what to do this these equations in this scenario. I have a lot of problems similar in concept to this one, but I just don't understand how to solve for them!

4. Oct 13, 2011

cepheid

Staff Emeritus
Yes, but how, specifically does it change? Hint: ignoring the mass of the person's arm, you can think of the mass that gets caught as being a point mass that is moving in a circle around the centre of rotation whose radius is the arm length. What is the moment of inertia of such a system? How does it combine with the moment of inertia of the person + stool?

Yes, but after the catch happens, is there linear motion any longer?