Deriving work-kinetic energy theorem for rotational motion

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Homework Help Overview

The discussion revolves around deriving the work-kinetic energy theorem for rotational motion, specifically the equation W=(0.5*I)*((ωf^2)-(ωi^2)) from the relationship W=τ*(θ). Participants are exploring the connections between work, torque, and rotational motion concepts.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to manipulate the equations relating work, torque, and rotational motion but expresses uncertainty about their correctness. Questions arise regarding the use of calculus and the definition of torque. Some participants suggest reconsidering the definitions and relationships between force, torque, and radius.

Discussion Status

Participants are actively engaging with the problem, questioning assumptions, and clarifying definitions. There is a recognition of potential errors in the original approach, and some guidance is offered regarding the correct relationships between the variables involved.

Contextual Notes

There is mention of constraints regarding the use of scalar versus vector multiplication, as well as the need to clarify the definitions of torque and force in the context of rotational motion.

gimak
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Homework Statement



How to derive W=(.5*I)*((ωf^2)-(ωi^2)) from W=τ*(θ)

Homework Equations



The two equations seen above (big W is work; little w is rotational velocity, τ is torque, alpha=rotational acceleration).

s=r*θ a=r*(alpha) (ωf^2)-(ωo^2)=2*(alpha)*(θ) F=r*τ F=ma

The Attempt at a Solution



W=T*(θ)=(F/r)*(s/r)=(r^-2)*F*s=(r^-2)*ma*s=(r^-2)*m*(r*alpha)((ωf^2)/(2*alpha))*r
=0.5*m*ωf^2

Obviously this isn't right. What went wrong?
 
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Are you allowed to use calculus?
 
gimak said:

Homework Statement



How to derive W=(.5*I)*((ωf^2)-(ωi^2)) from W=τ*(θ)

Homework Equations



The two equations seen above (big W is work; little w is rotational velocity, τ is torque, alpha=rotational acceleration).

s=r*θ a=r*(alpha) (ωf^2)-(ωo^2)=2*(alpha)*(θ) F=r*τ
[/QUOTE]

The formula in red is wrong. How is the torque defined?

ehild
 
response to ehlid

How is it wrong? Force is torque times radius, is it not. Oh, I can't use scalar multiplication on this. Do I have to use the cross product: F=t x r?
 
Or τ = I*α = I*a/r maybe...

and you should think of your s as Δs
 
gimak said:
How is it wrong? Force is torque times radius, is it not.

It is not. Check your textbooks.

ehild
 
correction

Shoot! I'm sorry! T=r*F. I got it backwards! If I plug in the right equation, the first equation will eventually turn into 0.5*m*(r^2)*(ωf^2)=I*(ωf^2).
 
Last edited:

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