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

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SUMMARY

Angular momentum is defined using the cross product of the position vector (r) and the momentum vector (p), expressed as r x p. This mathematical operation is essential because it accounts for the perpendicular direction of angular momentum, which is not captured by the dot product (r . p). The cross product inherently incorporates the directional aspect of rotational motion, making it the appropriate choice for calculating angular momentum.

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  • Knowledge of cross product and dot product operations
  • Basic principles of rotational dynamics
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CrazyNeutrino
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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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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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