Understqarnding equations for angular velocity

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Discussion Overview

The discussion revolves around understanding the equation for angular velocity, particularly in the context of converting rotational speed from revolutions per minute to radians per minute. Participants explore the definitions and relationships between angular velocity, angular displacement, and angular acceleration, while also addressing the conversion of units.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant expresses confusion about the equation for angular velocity, w = alpha/time, and questions how to apply it to a helicopter blade rotating at 400 revolutions per minute.
  • Another participant clarifies that for constant angular velocity, w equals angular displacement divided by time, and emphasizes the need to convert revolutions to radians.
  • A third participant provides the conversion method, stating that 400 revolutions per minute translates to 400 x 2π radians per minute, leading to a specific numerical result in radians per second.
  • One participant expresses difficulty with the concept of radians and asks if arc length is related to the equation, indicating a lack of familiarity with trigonometry.
  • Another participant explains that radians are defined based on the arc length in a circle, providing a geometric perspective to help clarify the concept.

Areas of Agreement / Disagreement

Participants generally agree on the need to convert revolutions to radians for proper understanding of angular velocity, but there remains some uncertainty and confusion regarding the application of these concepts, particularly for those less familiar with trigonometry.

Contextual Notes

Some participants express limitations in their mathematical background, which may affect their understanding of the concepts discussed. There is also an emphasis on the need for clarity in the relationship between angular velocity, angular displacement, and the conversion to radians.

LT72884
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I am having dificulty understanding the equation to angular velocity.

w=alpha/time

so if given this statement, (this is not homework). A helicopter blade is rotating at 400 rev per minute, find angular velocity in radians per minute.

So i have w=400/1 minute. great, so that's it? or is there more. if there is more, then why doesn't the equation state that. What am i supposed to do with 400/1? to me, that should be the answer because we did indeed find that w=alpha over time where alpha is 400 and time is 1 minute. I am soo lost. hahaha

thanks guys
 
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LT72884 said:
I am having dificulty understanding the equation to angular velocity.

w=alpha/time

so if given this statement, (this is not homework). A helicopter blade is rotating at 400 rev per minute, find angular velocity in radians per minute.

So i have w=400/1 minute. great, so that's it? or is there more. if there is more, then why doesn't the equation state that. What am i supposed to do with 400/1? to me, that should be the answer because we did indeed find that w=alpha over time where alpha is 400 and time is 1 minute. I am soo lost. hahaha

thanks guys
For constant angular velocity, w = angular displacement/time. For constant angular acceleration starting from rest, w = alpha*time, where alpha is the angular acceleration.

Your problem relates to constant angular velocity. You are correct in that it's angular velocity is 400 rev/min. But the problem asks you to convert it to radians/minute. So how many radians in a revolution?
 
Angular velocity is usually measured in radians per second. In one rotation the angle swept out is 360 degrees or 2xpi radians. So, if the rate of rotation is 400/minute, then the angular velocity would be 400 x 2xpi radians per minute which would be 800pi/60 = 40pi/3 radians/second.

Hope this helps,

John
 
arg, this whole radians thing confuses me. lol. so because it asked for it in radians, i use 2pi because in one revolution is 360* or 2pi. So is arc length related to this equation at all? please be easy. this is my first trig calss and i have not had math since 2002. please please be easy on me. I am struggling and need encouragement. haha. i did do algerbra last semester but that is no where near trig.

thank you sooooooooooooo much
 
Radians are 2*pi for a circle because that's the total arc length around the unit circle (radius = 1). When you scale it to a larger circle, then the arc length is just angle in radians * radius.
 
Re radians, imagine an isoceles triangle ABC (AB=AC) drawn inside a circle with point A at the centre and B and C are points on the circumference of that circle.
Replace side BC with the arc between B and C.

If the length of this arc = AB or AC, then the angle BAC is defined as 1 radian regardless of the length of AB.

daqddyo1
 

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