Centripetal Motion Velocity vs. Position Angle Assignment

[burtonjib]

1. Show that the angle between two position vectors is equal to the angle between two instantaneous velocity vectors eg. v₁ and v₂ when v₁ and v₂ are conncected tail to tail in a uniform circle. No angles are given, it is just general.



2. Has to be proven without calculus. No information is given other than the fact that the circle is uniform and therefore the speed is constant.



3. I didn't attempt the question because I'm not exactly sure how to go by proving that the angles are equal.

 

[obafgkmrns]

Do I understand you to be describing two particles in circular motion about a common central point? If so, then what is the angle between each particle's position vector and its velocity vector?

 

[burtonjib]

Yes that's exactly it. No angle was given though, the question is just asking to prove that the angle between position vectors is equal to that between the velocity vectors.

 

[obafgkmrns]

Try drawing a diagram. Draw arbitrary position vectors from a common point and then draw a velocity vector from the head of each position vector. Keep in mind that circular motion makes each velocity vector normal to its corresponding position vector.

 

[burtonjib]

I don't really see how that would show the equality between θ₁ and θ₂

 

[obafgkmrns]

If two lines intersect at an angle θ, at what angle do their normals intersect?