The figure below shows an overhead view of a uniform stick on which four forces

Question

The figure below shows an overhead view of a uniform stick on which four forces act. Suppose we choose a rotation axis through point O, calculate the torques about that axis due to the forces, and find that these torques balance. Will the torques balance if, instead, the rotation axis is chosen to be at (a) point A (on the stick), (b) point B (on line with the stick), or (c) point C (off to one side of the stick)? (d) Suppose, instead, that we find that the torques about point O do not balance. Is there another point about which the torques will balance?

Explanation / Answer

(a)
Will the torques balance if, instead, the rotational axis is chosen to be at point A
yes

(b)
Will the torques balance if, instead, the rotational axis is chosen to be at point B
yes

(c)
Will the torques balance if, instead, the rotational axis is chosen to be at point C
yes

(d)
Suppose, instead, that we find that the torques about point o do not balance. Is there another point about which the torques will balance?
no

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