Finding the movement equation (non intertial system)

[velvetmist]

Homework Statement

A particle of a mass ##m## is embedded in a circular rail, (radius: ##R##), without any friction. In a given moment, the particle finds itselfs without velocity at point C, and a force is applied on the rail, which starts moving with an ## \vec A ## constant acceleration. Use a non-inertial system fixed to the rail to solve the problem.

Arrange the Newton's equations, and find the movement equation of the particle.

(It was originally in spanish that's why I only screenshoted the graph)

Homework Equations

## \vec F' = m\vec a - m \vec A ##

The Attempt at a Solution

## \vec F_v = bending force ##

So I manage to integrate ##\ddot \varphi## so i get ##\dot \varphi (\varphi)##, but I guess i have to find ##\varphi (t)## to get the movement equation, and I'm really stuck at this point.

 

[kuruman]

What does your equation for ##\ddot{\varphi}## look like? Where is ##\varphi## measured from? I assume that the mass is instantaneously at rest relative to the circle's reference frame. It may help your thinking to consider that in a non-inertial frame accelerating with constant acceleration, there is an "effective" acceleration of gravity ##g_{eff.}## and find its magnitude and direction.