Newton's Laws
N1L: no force $\Rightarrow \vec{V}={\rm const}$ (or at rest, $\vec{V}=0$)
implies existence of inertial reference frames
N2L:
\[
\vec{a}={1\over m}\vec{F}_{\rm total}, \quad \mbox{or} \quad \sum \vec{F}= m \vec{a}
\]
implies that objects have mass, a measure of inertia
N3L: all forces are due to interactions
\[
\vec{F}_{\rm A\> on\> B} = - \vec{F}_{\rm B \> on \> A}
\]
Problem-solving strategy, refined
- read and re-read; itentify what is known/unknown
- make a drawing, or draw a vector diagram, identify all [pairs of] forces
- use the laws of Physics to establish formal relationships ($F=ma$), or
use N2L to determine acceleration, $\vec{a}={1\over m}\vec{F}_{\mbox{total}}$
- perform algebraic manipulations to get the final result, or
use kinematics, i.e. $\vec{a} \rightarrow \vec{V} \rightarrow \vec{r}$
- substitute numerical values; watch significant figures
- check units; does the result make sense?
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