Calculating KE in rotational motion

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Homework Help Overview

The problem involves calculating the total kinetic energy of a solid disk in rotational motion, specifically addressing both translational and rotational kinetic energy components.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the relationship between translational and rotational kinetic energy, questioning the adequacy of using only translational kinetic energy in the calculation. They explore the formula for rotational kinetic energy and its connection to angular speed.

Discussion Status

Some participants have provided guidance on incorporating both translational and rotational kinetic energy into the calculation. There is an acknowledgment of the importance of the moment of inertia in the context of the problem, and the discussion appears to be moving towards a clearer understanding of the concepts involved.

Contextual Notes

Participants are working under the assumption that the disk rolls without slipping, which is a critical condition for the relationship between translational and angular speeds.

MinaHany
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Homework Statement


A 20kg solid disk (I=1/2Mr^2) rolls on a horizontal surface at the rate of 4.0m/s
Calculate its total kinetic energy


The Attempt at a Solution


I think that simply equating the KE to (0.5)(m)(v^2) would be a wrong solution because then I would not use the moment of inertia given in the question, although I don't know why it is wrong.


Thank you.
 
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MinaHany said:
I think that simply equating the KE to (0.5)(m)(v^2) would be a wrong solution because then I would not use the moment of inertia given in the question, although I don't know why it is wrong.
It's wrong because it ignores the rotational KE. The rolling disk has both translational and rotational KE. What's the formula for rotational KE? Hint: How does translational speed relate to angular speed? (Assume it rolls without slipping.)
 
Use:

KE = KEtranslational + KErotational = (1/2)mvcm2 + (1/2)Iw2

vcm : velocity at the center of mass[sorry Doc Al, I didn't see you post]
 
Last edited:
Thank you Doc AL and lewando..
Your replies made the idea clear for me.
 

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