Uniform circular motion?

  • #1
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science2.PNG

How is Δθ in circle equals to angle in velocity vectors triangle?
I tried using simple geometry but I can't.
 

Answers and Replies

  • #2
Doc Al
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Try this:

What if r' were right on top of r? What is the angle between them? What is the angle between the velocity vectors?

Now move r' just a bit, an angle Δθ from r. How does the angle between the velocity vectors change?
 
  • #5
Delta2
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Its because they are angles that have sides vertical to each other. r' is vertical to v' and r is vertical to v so the angle of (r',r) equals the angle of (v',v).
 
  • #6
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Delta2 and Clara I appreciate your explaination but can you please describe some '90 degree usage'.
 
  • #7
Doc Al
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Another way to look at it: Realize that the velocity vectors are always 90° rotated compared to the r vectors. So if the angle that an r vector makes with the x-axis is θ, then the corresponding velocity vector must make an angle of θ + 90°.
 
  • #8
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Delta2 and Clara I appreciate your explaination but can you please describe some '90 degree usage'.

In the photo, θ+a = 90..(1) , a+b=90...(2), (1)-(2), θ=b , so it proves your statement "Δθ in circle equals to angle in velocity vectors triangle".
I hope it helps.
 
  • #9
James R
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One other point: the vector diagram on the right does not correspond to the vectors shown on the left.
Recall that ##\Delta \vec{v} = \vec{v}'-\vec{v}##. You also seem to have swapped the ##\vec{v}'## and the ##\vec{v}## in the diagram.
 

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