School of Mathematics and Statistics, The University of Sydney
 14. Line Vectors
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The moment of a line vector about a point

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When a force acts on a body it can cause it to move in a particular direction and it can also cause it to twist. (Think of a spanner or wrench turning a bolt.) In order to measure the twist we introduce the concept of the moment of a line vector about a point.

The moment of a line vector (l,v) about a point O is the - --> vectorOP × v, where P is a point on l.

It doesn’t matter which point P on l we choose because we get the same value of the moment for all points of l. To see this, suppose that Q is another point on l. Then -P-->Q is parallel to v and so -P-->Q × v = 0. Therefore,

-O-->Q × v = (-O-->P + -P-->Q) × v
= -OP--> × v + -P-->Q × v
= - --> OP × v.

l v O Q P

When calculating the moment of a line vector (l,v), the particular choice of the point P on l does not affect the answer but if you change the point O you will get a different result. This is why we always refer to the moment about a point O.

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Main menu Section menu   Previous section button disabled Line vectors and forces Systems of line vectors