Calculating Kinetic Energy with Rotational Motion

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Homework Help Overview

The problem involves a student on a rotating piano stool who catches a mass thrown to them, raising questions about the kinetic energy of the system before and after the catch. The subject area includes concepts of rotational motion and kinetic energy, particularly focusing on the moment of inertia and angular velocity.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the change in moment of inertia when the mass is caught and its implications for the kinetic energy of the system. There are inquiries about how rotational kinetic energy relates to moment of inertia and angular velocity, as well as the specific calculations needed for this scenario.

Discussion Status

Some participants have offered guidance on understanding the relationship between moment of inertia and kinetic energy, while others express confusion about applying the relevant equations. The discussion is exploring multiple interpretations of the problem, particularly regarding the effects of the mass being caught on the system's kinetic energy.

Contextual Notes

Participants are grappling with the implications of the mass being caught, including how it affects the moment of inertia and whether linear motion continues after the catch. There is a noted lack of clarity on how to apply the equations of motion in this context.

embudini
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Homework Statement


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.


Homework Equations


W=Kf-Ki
ω=v/r

The Attempt at a Solution



All I've gotten so far is Ki=3.6+.5*1.7*3^2=11.25 J. I'm really stuck, please help!
 
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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?
 
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!
 
embudini said:
The moment of inertia would increase because the system has a greater mass.

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?

embudini said:
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!

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

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