Radius of Curvature of a Train Turning North East

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SUMMARY

The discussion centers on the radius of curvature of a train turning towards the northeast. It establishes that the outer rail's radius of curvature is greater than that of the inner rail due to the physical width of the train. The conversation emphasizes that while the velocity and radial acceleration remain constant, the radius of curvature must account for the train's dimensions rather than treating it as a point mass. This distinction is crucial for understanding the dynamics of trains on curved tracks.

PREREQUISITES
  • Centripetal acceleration concepts
  • Understanding of radius of curvature
  • Knowledge of train dynamics and geometry
  • Familiarity with non-point mass physics
NEXT STEPS
  • Study the principles of centripetal acceleration in non-point masses
  • Explore the geometry of circular tracks and their impact on train dynamics
  • Investigate the effects of train width on curvature calculations
  • Learn about the physics of turning in large vehicles, specifically trains
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Engineers, physicists, and transportation planners interested in the dynamics of train movement and curvature effects on rail systems.

harini_5
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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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