How Do You Calculate Torque from Cross Product?

AI Thread Summary
To calculate torque using the cross product, the formula T = r × F is applied, where r is the position vector and F is the force vector. The user provided vectors F = (9.0 N) i + (-4.0 N) k and r = (3.0 m) j + (-1.0 m) k, leading to the calculation of torque. The resulting torque was computed as F × R, yielding values that the user found incorrect. The discussion included clarifications on handling cross products and emphasized the importance of treating them like any other product. Accurate calculations are essential for determining the correct torque values about specified points.
Nanuven
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Force F = (9.0 N) i hat + (-4.0 N) k hat acts on a pebble with position vector r = (3.00 m) j hat + (-1.0 m) k hat, relative to the origin.(a) What is the resulting torque acting on the pebble about the origin?
( N·m) i hat + ( N·m) j hat + ( N·m) k hat

(b) What is the resulting torque acting on the pebble about a point with coordinates (0.0 m, 0.0 m, 5.0 m)?
( N·m) i hat + ( N·m) j hat + ( N·m) k hat
So all I could come up with was cross product was that torque = r cross F

Therefore T = fRsin\theta

I looked up cross product on Wikipedia (not best site I know but w/e) and it came up with:

i x j = k
j x k = i
k x i = j

I tried those but it doesn't seem to be giving me the right answer. Any help please??

The Attempt at a Solution

 
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F = \[ \left[ \begin{array}{c} 9 \\\ 0 \\\ -4 \end{array} \right]\]

R = \[ \left[ \begin{array}{c} 0 \\\ 3 \\\ -1 \end{array} \right]\]

F \times R = \[ \left[ \begin{array}{c} F_2R_3-F_3R_2 \\\ F_3R_1-F_1R_3 \\\ F_1R_2-F_2R_1 \end{array} \right]\]

F \times R = \[ \left[ \begin{array}{c} -12 \\\ -9 \\\ -27 \end{array} \right]\]

I did this with software. I haven't hand checked it.
 
Last edited:
Nanuven said:
torque = r cross F

i x j = k
j x k = i
k x i = j

Hi Nanuven! :smile:

Also ii = jj = kk = 0.

Treat cross products just the same as any product.

For example:

(ai + bj)(cj + dk)

= acij + adik + bcjj + bdjk

= ack - adj + bdi. :smile:

(btw, use the B tag to do bold … if that doesn't work, type [noparse] before and after.[/noparse])
 
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