Finding an expression for torque

[Lucy Yeats]

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.

 

[Curious3141]

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\frac{dω}{dt} ---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\frac{dω}{dt}

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.

 

[Lucy Yeats]

Great, I've got the right answer now.

Thank you very much! :-)

 

[Curious3141]

Great, I've got the right answer now.

Thank you very much! :-)

You're welcome.