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Normal and centrifugal force for arbitrary curves

by Gavroy
Tags: arbitrary, centrifugal, curves, force, normal
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Gavroy
#1
Mar13-13, 05:41 PM
P: 235
Hi, i have a curve g:[0,t]->IRē with g(t)=(x(t),y(t)) in a homogenous gravitational field and i want to look at a ball rolling down this curve. therefore i want to derive some equations in order to calculate the normal force and the centripetal force at each point of this curve in order to see where the ball "leaves" the curve. therefore i am looking for an equation that gives me both forces just by using the parametrization of my curve. is there an equation for this?
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rcgldr
#2
Mar13-13, 09:03 PM
HW Helper
P: 7,032
This might help, the radius of curvature for a parametric curve is:

radius(t) = ( (x'(t))2 + (y'(t))2 )3/2 / | (x'(t) y''(t)) - (y'(t) x''(t)) |


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