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

1. Oct 4, 2014

### davidbenari

1. The problem statement, all variables and given/known data
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

2. Relevant equations
T=r x F

3. 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.

2. Oct 4, 2014

### Orodruin

Staff Emeritus
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.

3. Oct 4, 2014

### davidbenari

I dont 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 ?

4. Oct 4, 2014

### Orodruin

Staff Emeritus
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.

5. Oct 4, 2014

### 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?

6. Oct 4, 2014

### Orodruin

Staff Emeritus
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.

7. Oct 4, 2014

### davidbenari

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

8. Oct 4, 2014

### Orodruin

Staff Emeritus
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).