Understanding Velocity=r(omega)??

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In summary, the equation v=r(omega) represents the relationship between velocity and angular velocity, where v is velocity, r is radius, and omega is angular velocity given in radians per second. This can also be understood as the equation for arc length, s=theta*r, where s is arc length and theta is the central angle in radians. The definition of the radian is what ultimately leads to the equation v=r(omega), and this can be further understood by considering the equation for circumference, 2(pi)r, where r is the radius.
  • #1
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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  • #2
S=θr

where S is the Arc Length.

So think of it like r*θ/t
 
  • #3
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.
 
  • #4
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
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.
 

What is velocity?

Velocity is a measure of the rate of motion of an object. It is a vector quantity that includes both magnitude (speed) and direction.

What is the formula for velocity (r(omega))?

The formula for velocity is v = rω, where v is the velocity, r is the radius of the circular motion, and ω is the angular velocity (measured in radians per second).

How is velocity related to circular motion?

Velocity is related to circular motion because it is the rate at which an object moves around a circular path. The direction of the velocity vector is always tangent to the circle at any given point.

What is the difference between linear and angular velocity?

Linear velocity is the rate of change of an object's position in a straight line, while angular velocity is the rate of change of an object's angular position around a fixed point. Linear velocity is measured in meters per second (m/s), while angular velocity is measured in radians per second (rad/s).

How is velocity=r(omega) used in real life?

Velocity=r(omega) is used in many real-life applications, such as in the design and analysis of rotating machinery, vehicles, and sports equipment. It is also used in understanding and predicting the behavior of objects in circular motion, such as planets orbiting around the sun or electrons moving around an atom's nucleus.

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