# Centripetal acceleration geometry

1. Nov 7, 2009

### richardbsmith

This is probably a geometry question more that a physics question. I am trying to prove that in uniform circular motion $$\Delta$$ V$$/$$V= s$$/$$R.

I am basically trying to show that S forms a right triangle with $$\Delta$$V, when $$V{1}$$ is added to $$V{2}$$ as a vector. (This is to demonstrate that the triangles are similar.)

I understand that the angle formed by S and $$\Delta$$V is a right angle because it obviously inscribes the diameter. I just cannot seem to find a satisfactory proof that $$\Delta$$V must necessarily intersect the circle at the diameter.

Probably not explaining this very well.

2. Nov 8, 2009

### Lojzek

If you are solving geometry problems with both distances and velocities involved, then you
are probably making a mistake: remember that they have different units! (unless you study relativistic theory)
For the mentioned problem you should use formulas:
s=R*fi (fi is angle of the part of orbit traveled in radians)
$$\Delta$$V=V*sin(fi') (fi' is the angle between the old and new velocity vector)

Prove that fi=fi' and use sin(fi)=fi (for small angles) and you will get $$\Delta$$ V$$/$$V= s$$/$$R

3. Nov 8, 2009

### richardbsmith

Thank you so much for responding. I think though my question which started with uniform motion and delta V, is now simply a geometry question.

I will try to put up a drawing of what I so pitifully tried to explain.

Here is another image with a different angle and size of the tangents.

I have tried several approaches, but I cannot prove that the angle formed from tangent 1 to tangent 2 to the circle must inscribe a 180 degree arc and must be a right angle.

4. Nov 9, 2009

### A.T.

From : http://en.wikipedia.org/wiki/Inscribed_angle_theorem
So, to get an inscribed angle of 90° you need a central angle of 180°(=diameter line).

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