V = r times omega

  • Thread starter johnps
  • Start date
  • #1
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Homework Statement


I do not understand why velocity is equal to the radius times the angular velocity. Angular velocity is given in radians per second. How does this equal velocity when multiplied by the radius?

Thanks yall! I'm new here by the way.


Homework Equations


v=r(omega)


The Attempt at a Solution




??
 

Answers and Replies

  • #2
47
0
S=θr

where S is the Arc Length.

So think of it like r*θ/t
 
  • #3
berkeman
Mentor
59,016
9,110

Homework Statement


I do not understand why velocity is equal to the radius times the angular velocity. Angular velocity is given in radians per second. How does this equal velocity when multiplied by the radius?

Thanks yall! I'm new here by the way.


Homework Equations


v=r(omega)


The Attempt at a Solution




??
What is the equation for the diameter of a circle, in terms of the radius? That should help it to make more sense.

Welcome to the PF, BTW.
 
  • #4
ideasrule
Homework Helper
2,266
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By definition, s=θr. By definition, w=dθ/dt. That's why ds/dt=r*dθ/dt=r*w=v. Why the definition s=θr, you ask? That's how the radian was defined. It's simple, elegant, and leaves out a pesky constants that clutter up equations.
 
  • #5
2
0
Aha, so s=(theta)(radius) because of the equation circumference = 2 (pi) (r) correct?

Sorry I'm not sure how to get the symbols yet. I'll figure it out.
 

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