Forces25.pdf - (c Hang a weight W/2 a distance 2d to the...

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(c) Hang a weight W/2 a distance 2d to the right of the pivot (d) Hang a weight W α a distance / d α to the right of the pivot. Four ways to balance the beam These simple experiments suggest that the turning tendency of a force about some point is equal to the distance from the point multiplied by the force. This is certainly consistent with O = × M r F To see where the cross product in the definition comes from, we need to do a rather more sophisticated experiment. Let’s now apply a force F at a distance d from the pivot, but now instead of making the force act perpendicular to the pivot, let’s make it act at some angle. Does this have a turning tendency Fd? A little reflection shows that this cannot be the case. The force F can be split into two components – sin F θ perpendicular to the beam, and cos F θ parallel to it. But the component parallel to the beam will not tend to turn the beam. The turning tendency is only sin dF
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