Radius of Curvature of a Train Turning North East

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When a train turns from north to northeast, the outer rail's radius of curvature is greater than that of the inner rail due to the geometry of the track. The inner and outer rails are both circular, but the outer rail's radius exceeds the inner rail's by the width of the train. The discussion emphasizes that the equations for centripetal acceleration apply to point masses, while a train should be considered as a non-point mass, focusing on its center of mass. The velocity and radial acceleration remain consistent across both rails, but the curvature differences arise from their respective radii. Understanding these principles clarifies the dynamics of train movement on curved tracks.
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A train is moving towards north at one place.
it turns towards north east.
here we observe that the radius of curvature of outer rail will be greater than that of inner rail
why?pls explain
velocity and radial acc. are the same and radius of curvature=v^2/a normal
 
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I think you are focusing too much on the equations here...

if you consider a train going about a circular track, the inner and outer rail of the track will both be circular, but the outer rail will have a radius greater than the inner rail by the width of the train.

this is all this statement is saying.

in the equation for centripetal accelleration the radius is assuming a point particle, which a train is not.

the same equation is true for a non-point-mass where the radius is then for the center of mass.
 
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