Moment of inertia, conservation of angular momentum and energy

[volodymyr379]

Homework Statement

Student A, of mass 100 kg, stands 2 meters from the center of a circular platform which is free to rotate on frictionless bearings. Student B, not standing on the platform, tosses student A a baseball of mass 0.09 kg, which reaches student A with a velocity of 20 m/s directed perpendicular to the line joining student A and the center of the platform. If the platform has a moment of inertia 200 kg·m^2, what is its approximate angular velocity after student A catches the baseball?

Relevant Equations

mb*vb*r= (Ip+Is)*ω , where mb - mass of the ball, vb - speed of the ball, Ip and Is - moments of inertia of the platform and the student respectively.
E_kin = E_rot
(mb*v^2) = ((Ip+Is)*ω^2)/2

When I solved the problem using the conservation of angular momentum, I have got the correct result (ω = 0.006 rad/s). However, when I tried to find the answer using the conservation of energy the result was incorrect and I do not understand why.

 

[gneill]

Hi volodymyr379. Welcome to Physics forums.

Can you classify the type of collision that occurs when Student A catches the ball? What things are conserved in such a collision?

 

[volodymyr379]

Hi gneill.
No, unfortunately, I can't. The type of collision was not specifically stated in the problem. However, even if the collision is inelastic, it is hard for me to imagine that most of the kinetic energy of the ball would be transferred into heat, sound, etc. Using the conservation of energy I get that ω = 0.24 rad/s (instead of 0.006).

 

[gneill]

The collision must be inelastic since student A catches and retains the ball. Despite what may seem incredible, the energy will be lost.

 

[haruspex]

it is hard for me to imagine that most of the kinetic energy of the ball would be transferred into heat

Humans are far less sensitive to heat energy than to sound, light or KE. Try dropping a soft mass (so there's little sound) onto a hard surface repeatedly and notice how little it warms.

 

[FactChecker]

As a sanity check of your result ($\omega$ = 0.24 rad/s) using conservation of energy, notice that the platform would be rotating VERY FAST after the ball is caught.