Understanding Angular Velocity: W = 2pi(f) ?

In summary, angular velocity (w) is equal to 2pi multiplied by the frequency (f). The frequency represents the number of rotations or cycles in a period of time, while angular velocity measures the angle covered in that time. This equation takes into account the different units used for frequency (revolutions or cycles) and angular velocity (radians).
  • #1
mlostrac
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Can anyone explain to me how angular velocity (w) = 2pi(f) -->where f = frequency.

This is not a homework question involving numbers. I'm reading a section on "the period of sinusoidal Nature of SHM" and I don't understand how they get this equation.
 
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  • #2
frequency-number of rotations in a period of time, usually one s
w-angular velocity-angle in an amount of time
2pi-one full circle
hence w=2pif
 
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  • #3
In case the previous explanation was not quite clear: f and ω use different units to express the frequency. f expresses the frequency in terms of revolutions or number of complete cycles, while ω uses radians. 1 revolution is 2π radians (or 360 degrees), hence the factor of 2π in the relation between f and ω.
 

1. What is angular velocity?

Angular velocity is a measure of how quickly an object rotates around a fixed axis. It is typically denoted by the symbol ω (omega) and is measured in radians per second (rad/s).

2. How is angular velocity related to frequency?

Angular velocity (ω) is equal to 2π times the frequency (f) of rotation. This relationship is expressed by the equation ω = 2πf.

3. What is the unit of angular velocity?

The unit of angular velocity is radians per second (rad/s). This unit is used because it represents the angle (in radians) that an object rotates in one second.

4. What is the difference between angular velocity and linear velocity?

Angular velocity measures the rate of rotation of an object around a fixed axis, while linear velocity measures the rate of change of an object's position in a straight line. Angular velocity is measured in radians per second, while linear velocity is measured in meters per second.

5. How is angular velocity calculated?

Angular velocity is calculated by dividing the angular displacement (change in angle) by the time taken for that displacement. This can be expressed by the equation ω = Δθ/Δt, where ω is angular velocity, Δθ is angular displacement, and Δt is time.

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