# Torque and vectors

1. Jul 6, 2014

### lukatwo

1. The problem statement, all variables and given/known data
So I was wondering how do we account for vectors that are at a certain angle. The problem that I'm having with the picture is: if I was calculating torque from point B, how would I account for the vector G.

2. Relevant equations

3. The attempt at a solution
I've tried taking the component that's vertical to the slope, but in that case what is the lever arm? Is it where the vector G crosses the slope(point D)?

2. Jul 6, 2014

### SammyS

Staff Emeritus
Try taking the component that's perpendicular to the ramp (incline).

Do you know about the line of action for a force -- in this case force G ?

3. Jul 6, 2014

### lukatwo

I've tried taking the perpendicular component, but not sure what the lever arm is. I'm not sure how to determine the line of action.

4. Jul 6, 2014

### electronicsguy

By extending the force T, you can see that it will contact point D. So it is like you're applying the force T directly on point D and the lever arm will be BD. Then take the perpendicular component of force T relative to the slope.

You can always check.
If we assume that BT is perpendicular to force T (note: BT is the dist. bet. B and T)
From the figure, the τ = T*(BT) . But, BT = BDsin(90-α). Therefore τ = T*(BDsin(90-α)) [1].
Returning to your problem, τ = Txr where r is the lever arm. The perpendicular component of T is Tsin(90-α). Therefore τ = Tsin(90-α)*r = T*(BDsin(90-α)) from [1]. Therefore r = BD.