Understanding Velocity=r(omega)??

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Homework Help Overview

The discussion revolves around the relationship between linear velocity and angular velocity, specifically the equation v = r(ω). Participants express confusion about how angular velocity, measured in radians per second, translates to linear velocity when multiplied by the radius.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Some participants attempt to relate the equation to the concept of arc length and the definitions of angular velocity. Others question the foundational definitions, such as the relationship between the radius and the circumference of a circle.

Discussion Status

The discussion is ongoing, with participants exploring various definitions and relationships. Some have provided insights into the definitions of arc length and angular velocity, while others are still seeking clarity on the underlying concepts.

Contextual Notes

Participants note their newness to the forum and express uncertainty about mathematical symbols, indicating a potential barrier to fully articulating their thoughts.

johnps
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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




??
 
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S=θr

where S is the Arc Length.

So think of it like r*θ/t
 
johnps said:

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.
 
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.
 
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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