Understanding Velocity=r(omega)??

[johnps]

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

??

 

[Redd]

S=θr

where S is the Arc Length.

So think of it like r*θ/t

 

[berkeman]

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.

 

[ideasrule]

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.

 

[johnps]

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.