Euler's First Law and the Conservation of Momentum

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Euler's first law, which defines linear momentum as the product of mass and velocity of a body's center of mass, primarily applies to single bodies. However, the discussion raises the question of whether it can be extended to systems of bodies or if conservation of momentum should be used instead. Internal forces within a system do not affect the total momentum, suggesting that Euler's law can be relevant for collections of bodies. The distinction between Newton's laws, which focus on particles, and Euler's laws, which apply to bodies, is emphasized. Ultimately, the conversation highlights the complexity of applying these principles to systems of multiple bodies.
e2m2a
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I know Euler's first law applies to a single body, but can we use it for a system of bodies? Or should we invoke the conservation of momentum to obtain the same result for a system of bodies?
 
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Hi e2m2a! :smile:
e2m2a said:
I know Euler's first law applies to a single body, but can we use it for a system of bodies? Or should we invoke the conservation of momentum to obtain the same result for a system of bodies?

hmm … i had to look this up in "[URL :redface:, so let's copy it for everyone's benefit …
Euler's first law states that the linear momentum of a body is equal to the product of the mass of the body and the velocity of its center of mass: L = mvc.o.m. Internal forces, between the particles that make up a body, do not contribute to changing the total momentum of the body. The law is also stated as F = maG

(it means we can ignore any rotation, so long as we deal only with the centre of mass :wink:)

I don't really understand your question …

surely a system of bodies is a body …

Newton's first two laws are about particles, while Euler's two laws are about collections of particles (called "bodies"), and a collection of collections is still a collection?
 
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