Math Is Fun Forum

ilovealgebra

Member

Registered: 2006-10-02

Posts: 40

Vector-Valued Functions

Hey guys just a quick question.

Suppose that r(t) = (kcos(wt), ksin(wt))

Is the position vector of a particle rotating around the origin in a circle of radius k and angular velocity w.
Show that the acceleration of the particle is directed at the origin , with magnitude v^2/k, where v is the
speed of the particle

Can someone please go through this, thanks for the help

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"...nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called into question (much less condemned) upon the testimony of biblical passages."
-Galileo Galilei

hermit

Member

Registered: 2010-02-16

Posts: 4

Re: Vector-Valued Functions

I have not done problem like this in a long time, but think I remember the strategy:

Fix an arbitrary point on the circle. Compute the tangent vector at this point. The magnitude of this vector is the speed. Then differentiate the tangent vector to obtain the normal vector at the point. The normal vector will always point toward the center, this should be evident in the expression for normal vector.