Finding torque: With respect to origin, with respect to y-axis.

[davidbenari]

Homework Statement

Find the torque at point (1,5,2), first with respect to the origin and then with respect to the y-axis.
F=2i-3j+k

Homework Equations

T=r x F

The Attempt at a Solution

Torigin= 11i+3j-13k ; Tyaxis=6i+3j-3k here I defined a new vector r'=1i+2k

What I don't understand is what exactly "torque with respect to y axis" means. Does it mean I have a gigantic cylinder, laying around my axis and can only rotate in that direction? What does it mean? How does one interpret the fact that you can have multiple torques if you define new references?

Thanks. Sorry if this question is dumb.[/B]

 

[Orodruin]

The "torque wrt the y axis" is the y-component of the torque at any point on the y-axis. This is independent of the actual point on the y-axis and you can chose either the origin or the point on the axis closest to the point where the force is applied (or any other point on the y-axis). Note that you can see this in your attempted solution where the y-component is 3 in both cases.

 

[davidbenari]

I don't understand. I don't see how its the y-component of the torque. Are you saying my answer should only have one component? like Tyaxis=3j ?

 

[Orodruin]

The torque with respect to an axis is a single number (if something is allowed to turn only around that axis, it is the only relevant torque).

Edit: Compare the situation to the case when things are confined to a plane and there is only one relevant torque.

 

[davidbenari]

Nice, thanks. It could also be a vector, or does it necessarily have to be just a number? Also, when I'm asked "with respect to the origin" then that means its not confined to any particular axis right?

 

[Orodruin]

You could also quote the projection of the momentum onto the y-axis - although the direction is superfluous when you are talking about the projection onto a one-dimensional subspace. When you talk about torque wrt a point you are not necessarily confining it to rotate in one direction only and should quote the full torque vector.

 

[davidbenari]

But why would the direction be superfluous in 1-D if the torque can be clockwise or anticlockwise? Thanks again.

 

[Orodruin]

You simply define one direction as the positive one (in this case, the positive y-direction is as good a choice as any). If the torque is in the other direction, then the value will be negative (as will the value of the projection).