Finding an expression for torque

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    Expression Torque
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Homework Help Overview

The discussion revolves around finding an expression for torque in the context of angular momentum and its relation to angular velocity. The problem is situated within mechanics, specifically dealing with the dynamics of rotational motion.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between torque and angular momentum, exploring the equations T = dJ/dt and T = I dω/dt. There is an attempt to solve a differential equation involving angular velocity and torque, with some questioning the implications of the negative sign in the torque equation.

Discussion Status

Some participants have shared their attempts at solving the problem, with one indicating they have arrived at the correct answer. However, the discussion does not reflect a consensus on the methods used, and various interpretations of the equations are still being explored.

Contextual Notes

There are references to specific equations and the importance of applying bounds using definite integrals, indicating that the problem may have constraints or specific conditions that need to be considered.

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Homework Statement



http://www.physics.ox.ac.uk/users/yassin/mechanics/problems/probs6_2011.pdf

Q 2b.

Homework Equations





The Attempt at a Solution



T is torque and J is angular momentum.
T=dJ/dt=I dω/dt

I tried solving dω/dt=ωk to get dω/dt=ce^kt, but this may not help.
 
Last edited by a moderator:
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Lucy Yeats said:

Homework Statement



http://www.physics.ox.ac.uk/users/yassin/mechanics/problems/probs6_2011.pdf

Q 2b.

Homework Equations


The Attempt at a Solution



T is torque and J is angular momentum.
T=dJ/dt=I dω/dt

I tried solving dω/dt=ωk to get dω/dt=ce^kt, but this may not help.

They represented torque as N.

You're given N = kω ---equation 1

You also know that N = -I[itex]\frac{dω}{dt}[/itex] ---equation 2
(the negative sign is to keep N positive since they're concerned with the numerical value for torque).

You can equate equations 1 and 2 to get kω = -I[itex]\frac{dω}{dt}[/itex]

and solve the differential equation. Remember to apply the given bounds using definite integrals on both sides after separating the variables ω and t.

After that, express k in terms of the other variables, and put this back into equation 1 to get N.
 
Last edited by a moderator:
Great, I've got the right answer now.

Thank you very much! :-)
 
Lucy Yeats said:
Great, I've got the right answer now.

Thank you very much! :-)

You're welcome. :smile:
 

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