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The radius of curvature in railways quantifies how fast the track is changing direction. It is the radius of a circle that matches the particular section of track involved.
This information is important for many reasons.
It is used to calculate the maximum speed that a train can have when entering the curve. Part of this is knowing how rapidly the radius changes - usually a curved section of track is gradually tightened up so that the left-right acceleration of the train does not change suddenly.
It is used to calculate the maximum deviation from centerline that a train will have going through the curve, due to the fact that each car has a set distance between wheels and the car will be a chord on the circle of track. That has application in positioning platforms in relation to tracks, and in positioning curved tracks that are adjacent to other curved tracks.
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Center of curvature in differential calculus?
Center of curvature = r(t) + (1/k)(unit inward Normal) k = curvature Unit inward normal = vector perpendicular to unit tangent r(t) = position vector
How do you draw an arc with a given length and known radius?
The length of an arc equals he angle (in radians) times the radius. Divide the length by the radius, and that gives you the ange. Measure out the angle on a protractor and draw the length of the radius at the begining and end of the angle. Then draw theportion of the circle with its center at the location ofthe angle and extending out to the radius.
How do you find points of inflection in calculus?
Points of inflection on curves are where the curvature changes sign, such as when the second deriviative changes sign
What are some applications of differentiation in real life?
Yes if it was not practical it was not there. You can see the real life use on this link http://www.intmath.com/Applications-differentiation/Applications-of-differentiation-intro.php
How do you find the circumfrence of a circle when you have the area?
Divide the area by pi then square root your answer which will give the radius of the circle and use 2*pi*radius to find the circumference.
