Forest UCM MiNF
Mechanics in Noninertial Reference Frames
Linearly accelerating reference frames
Let [math]\displaystyle{ \mathcal S_0 }[/math] represent an inertial reference frame and \mathcal S represent an noninertial reference frame with acceleration [math]\displaystyle{ \vec A }[/math] relative to [math]\displaystyle{ \mathcal S_0 }[/math].
Ball thrown straight up
Consider the motion of a ball thrown straight up as viewed from [math]\displaystyle{ \mathcal S }[/math].
Using a Galilean transformation (not a relativistic Lorentz transformation)
At some instant in time the velocities add like
- [math]\displaystyle{ \dot {\vec r} = \dot {\vec {r}_0} - \vec V }[/math]
where
- [math]\displaystyle{ \vec V }[/math] = velocity of moving frame [math]\displaystyle{ \mathcal S }[/math] with respect to [math]\displaystyle{ \mathcal S_0 }[/math] at some instant in time