30 lines
768 B
Markdown
30 lines
768 B
Markdown
# Momentum
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> *Definition 1*: the **momentum** $\mathbf{p}$ of a particle is defined as the product of the mass and velocity of the particle
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>
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> $$
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> \mathbf{p} = m \mathbf{v},
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> $$
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>
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> with $m$ the mass of the particle and $\mathbf{v}$ the velocity of the particle.
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For the case that $\mathbf{v}: t \to \mathbf{v}(t) \implies \mathbf{v}'(t) = \mathbf{a}(t)$ we have the following theorem.
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> *Theorem 1*: let $\mathbf{v}$, $\mathbf{a}$ be the velocity and acceleration of a particle respectively, if we have
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>
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> $$
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> \mathbf{v}: t \to \mathbf{v}(t) \implies \forall t \in \mathbb{R}: \mathbf{v}'(t) = \mathbf{a}(t),
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> $$
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>
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> then
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>
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> $$
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> \mathbf{p}'(t) = \mathbf{F}(t),
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> $$
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>
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> for all $t \in \mathbb{R}$.
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??? note "*Proof*:"
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Will be added later.
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