Why Does Angular Momentum Use a Cross Product Instead of a Dot Product?

Thread starter CrazyNeutrino
Start date Oct 20, 2012
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Angular Angular momentum Momentum

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Angular momentum is defined using a cross product because it incorporates the direction of the vectors involved, specifically the position vector and momentum vector. The formula r x p reflects the perpendicular relationship between these vectors, which is essential in determining the rotational effect. In contrast, a dot product does not account for direction, making it unsuitable for angular momentum calculations. The use of a cross product ensures that the resulting angular momentum vector is orthogonal to the plane formed by the position and momentum vectors. This fundamental distinction is crucial for accurately describing rotational dynamics.

Oct 20, 2012

CrazyNeutrino

Can someone please explain why angular momentum involves a cross product?

Why is it r x p and not r . P
Why a cross product and not a dot product?

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Oct 20, 2012

Rajini

Hi,
Angular momentum involves a perpendicular direction, i.e. in general when you take direction into account, it should be a cross product. In dot product no direction.
Cheers, Rajini

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