waseemshahzada

01-28-2012, 06:02 AM

show that the curvature of a circle of radius 'a' equals 1/a

plz help me if any body can solve it plz

plz help me if any body can solve it plz

View Full Version : show that the curvature of a circle of radius 'a' equals 1/a

waseemshahzada

01-28-2012, 06:02 AM

show that the curvature of a circle of radius 'a' equals 1/a

plz help me if any body can solve it plz

plz help me if any body can solve it plz

pka

01-28-2012, 10:10 AM

show that the curvature of a circle of radius 'a' equals 1/a

Let r(t)=a\cos(t)+a\sin(t) be a circle of radius a.

Then \bf{T}(t)=\dfrac{r'(t)}{\|r'(t)\|}.

Then curvature is \kappa(t)=\dfrac{\|\bf{T}'(t)\|}{\|r'(t)\|}.

Now you do the work.

Let r(t)=a\cos(t)+a\sin(t) be a circle of radius a.

Then \bf{T}(t)=\dfrac{r'(t)}{\|r'(t)\|}.

Then curvature is \kappa(t)=\dfrac{\|\bf{T}'(t)\|}{\|r'(t)\|}.

Now you do the work.

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