What is the new position vector if the reference point is changed to (0,4)?

[tmgrich]

A particle is located at the vector position r = (i + 3 j) m, and the force acting on it is F = (5 i + 6 j) N.
(a) What is the torque about the origin?
(b) What is the torque about the point having coordinates (0, 4) m?

when you are given an i + j, do you assume that it starts at the origin?
then to you add 4 to the j vector since you are changing the point to (0,4)?

 

[chroot]

Torque is defined as the cross product r x F, right?

You're given two vectors: r = (i + 3j) m, and F = (5i + 6j) N.

It sounds to me like you're missing the crucial ingredient that the representation r = (i + 3j) is the same as the "vector notation" (1, 3, 0); the representation (5i + 6j) is the same as (5, 6, 0). Can you calculate the vector cross product of those two vectors?

- Warren

 

[Ebolamonk3y]

Use matrix

 

[Doc Al]

when you are given an i + j, do you assume that it starts at the origin?

Yes, assume that the "position vector" is with respect to the origin (0,0,0).

then to you add 4 to the j vector since you are changing the point to (0,4)?

Since torque is always calculated with respect to (wrt) some point*, when you change that point from (0,0) to (0,4) you must use a new position vector with respect to that new reference point:
Let A = position of particle wrt 0,0 = 1,3
Let B = position of new reference point wrt 0,0 = 0,4
Let C = position of particle wrt 0,4 = ?
You know that A = B + C, so figure out the new position vector C.

*assumed to be in the z = 0 plane in this problem