(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 2D rotating coordinate system (x,y) is defined by:

[tex]x=Xcos\omega t+Ysin \omega t[/tex]

[tex]y=-Xsin\omega t+Y cos \omega t[/tex]

Where (X,Y) is the coordinate of the inertial frame and omega is some angular frequency. What is the force required to keep a mass m moving in a "straight" line (x,y)=(ut,0) where u is a constant?

2. Relevant equations

[tex]F=m\frac{d^2x}{dt^2}[/tex]

and the given equations of the new coordinates.

3. The attempt at a solution

Let me take the derivative of the given equations twice:

[tex]\frac{d(Xcos\omega t+Ysin \omega t)}{dt}=-X\omega sin \omega t + Y \omega cos \omega t=\omega y[/tex]

[tex]\frac{d^2x}{dt^2}=\omega \frac{dy}{dt}=\omega \frac{d(-Xsin\omega t+Y cos \omega t)}{dt}= \omega \left ( -\omega X cos \omega t -\omega Y sin \omega t \right)= -\omega^2 x [/tex]

Similarly:

[tex]\frac{dy}{dt}=-\omega x[/tex]

[tex]\frac{d^2y}{dt^2}=-\omega^2 y[/tex]

So we have:

[tex]F_x=-m \omega^2x[/tex]

[tex]F_y=-m \omega^2y[/tex]

Um... is this some kind of a spring force?

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# Homework Help: Rotating coordinates

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