IP A student sits at rest on a piano stool that can rotate without friction. The

Question

IP A student sits at rest on a piano stool that can rotate without friction. The moment of inertia of the student-stool system is 4.3 kgm2 . A second student tosses a 1.5 kg mass with a speed of 2.7 m/s to the student on the stool, who catches it at a distance of 0.40 m from the axis of rotation.

1. Does the kinetic energy of the mass-student-stool system increase, decrease, or stay the same as the mass is caught?

2. Calculate the initial kinetic energy of the system.

3. Calculate the final kinetic energy of the system.

Explanation / Answer

I will treat the tossed mass as a point mass caught exactly perpendicular between the radies and catch point
The total inertia is the sum of the individual inertias.

(I + md1² + md1²)w1 = (I + md2² + md2²)w2

w2 = (I + 2md1²)w1/(I + 2md2²

Conservation of angular momentum

=v/r

1.5*0.40^2*2.7/0.40=(4.3+1.5*0.40^2)*
solve for

=(1.5*0.40^2*2.7/0.40)/(4.3+1.5*0.40^2)

=.35 rad/s

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