A force having components is applied at point

PHYSICS · Subjective · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

12\,\text{N}

force having components

\vec F = 6\hat i + 9\hat j -3\hat k\,\text{N}

is applied at point

A(1\,\text{m},2\,\text{m},-1\,\text{m})

. The reference point is changed from the origin

O

to point

B(3\,\text{m},-1\,\text{m},2\,\text{m})

. (a) Obtain the position vector of point

A

with respect to the new origin

B

. (b) Hence calculate the moment (torque) of the force about point

B

. (c) Verify that the magnitude of the torque obtained in part (b) is equal to the magnitude that would be calculated directly from

\vec F\times(\vec r_A-\vec r_B)

, where

\vec r_A

and

\vec r_B

are the position vectors of

A

and

B

with respect to

O