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