Normal and centrifugal force for arbitrary curves

by Gavroy
Tags: arbitrary, centrifugal, curves, force, normal
Gavroy is offline
Mar13-13, 05:41 PM
P: 232
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 is offline
Mar13-13, 09:03 PM
HW Helper
P: 6,931
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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