Pedal Angular Velocity: Pi/2*f or 2pi*f?

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Discussion Overview

The discussion revolves around the angular velocity of a pedal mechanism that sweeps through an angle of pi/2 during one complete cycle. Participants explore the relationship between the pedal's angular displacement and its frequency of operation, considering the implications of the pedal's motion in the context of a sewing machine mechanism.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions how a complete cycle can be defined as pi/2 and asks for clarification on the geometry involved.
  • Another participant explains that the pedal operates as part of a four-bar linkage system, where the upper flywheel rotates through 2pi while the pedal only sweeps through pi/2.
  • There is a suggestion that the angular velocity should be calculated as angular distance divided by time, leading to a discussion about the correct interpretation of frequency in relation to angular displacement.
  • Some participants assert that the angular velocity is 2pi*f, despite the pedal not sweeping through a full 2pi, while others argue that it should be based on the actual angular distance of pi/2.
  • Clarifications are made regarding the definition of frequency and its application to the pedal's motion, with emphasis on the distinction between half periods and full cycles.

Areas of Agreement / Disagreement

Participants express differing views on the calculation of angular velocity, with some supporting the idea that it should be based on pi/2 and others insisting on the use of 2pi*f. The discussion remains unresolved, with no consensus reached on the correct approach.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the pedal's motion and the definitions of frequency and angular velocity. The relationship between the pedal's angular displacement and the flywheel's motion is also a point of contention.

max3
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So I've got a pedal which sweeps through pi/2 in 1 complete cycle (frequency is known). Is its angular velocity (pi/2)*f or 2pi*f just the same? (considering that it doesn't sweep through 2pi but pi/2)
 
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max3 said:
So I've got a pedal which sweeps through pi/2 in 1 complete cycle (frequency is known). Is its angular velocity (pi/2)*f or 2pi*f just the same? (considering that it doesn't sweep through 2pi but pi/2)

Welcome to the PF.

How can one complete cycle be PI/2? What is the geometry involved?
 
well the mechanism itself is the lower half of a pedal operated sewing machine. you may think of it as a four-bar linkage or a 'double crank'. while the upper flywheel rotates through 2pi, the pedal (connected by a rod) does not. I am given the frequency of operation of the pedal and need to know the pedal's angular velocity at 1 instant (assuming angular acceleration = 0).
 
max3 said:
well the mechanism itself is the lower half of a pedal operated sewing machine. you may think of it as a four-bar linkage or a 'double crank'. while the upper flywheel rotates through 2pi, the pedal (connected by a rod) does not. I am given the frequency of operation of the pedal and need to know the pedal's angular velocity at 1 instant (assuming angular acceleration = 0).

Ah, so the pedal rotates through PI/2 as the flywheel rotates through PI. So the angular velocity of the pedal is angular distance traveled divided by the time it takes to travel through that angular distance, right? What does that give you for an answer?
 
That's what I figured but many have contradicted me in saying that the angular velocity is 2PI*f irrespective of the pedal NOT sweeping through 2PI. Many thanks for your feedback.
 
max3 said:
That's what I figured but many have contradicted me in saying that the angular velocity is 2PI*f irrespective of the pedal NOT sweeping through 2PI. Many thanks for your feedback.

Be a little careful with the "f" part, though.

"f" refers to a frequency, or number of somethings per second. For circular motion, it would normally refer to the number of rotations per second. If one cycle is the pedal going down and coming back up, then there are two half periods per cycle. The angular velocity is the angular distance divided by the time taken, so the angular velocity of the pedal is the PI/2 traveled in one half of the period of the system (not the whole period).

Does that make sense?
 
berkeman said:
The angular velocity is the angular distance divided by the time taken, so the angular velocity of the pedal is the PI/2 traveled in one half of the period of the system (not the whole period).

Does that make sense?

Yes, only that a half period would correspond to PI/4 and not PI/2 as you state since in my case PI/2 is swept in 1 full cycle. Many thanks.
 

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