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Math Help - Angular Speed and Velocity Problem

  1. #1
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    Angular Speed and Velocity Problem

    A circle of radius 8 in. is rotating 15o/sec. What is the linear speed v, the angular speed in RPM and the angular speed in rad/sec?

    So at first I tried converting the 15o/sec to velocity, by having the degrees become inches. This will then have the measurement in/sec.
    But one thing I am confuse is with converting 15o to inches, can anyone help?
    Last edited by Chaim; March 11th 2012 at 08:24 PM.
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  2. #2
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    Re: Angular Speed and Velocity Problem

    Quote Originally Posted by Chaim View Post
    A circle of radius 8 in. is rotating 15o/sec. What is the linear speed v, the angular speed in RPM and the angular speed in rad/sec?

    So at first I tried converting the 15o/sec to velocity, by having the degrees become inches. This will then have the measurement in/sec.
    But one thing I am confuse is with converting 15o to inches, can anyone help?
    you cannot convert degrees to inches .. they are not the same type of measurement. degrees are an angle measure; inches are a measure of length.

    start by converting degrees to radians ... (degrees) \cdot \frac{\pi}{180} = radians

    once you have angular speed, \omega , in radians/sec, then linear speed , v = r\omega


    to convert angular speed from radians per second to RPM ...

    \left(\frac{radians}{sec}\right) \cdot \left(\frac{1 \, revolution}{2\pi \, radians}\right) \cdot \left(\frac{60 \, sec}{min}\right) = \frac{revolutions}{min}
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    Re: Angular Speed and Velocity Problem

    Thanks! That makes so much sense now
    But I was wondering, when I'm converting degrees into radians, why would that be the angular speed? Just wondering, cause I checked the internet of converting degrees, but do not understand how I would know that would be the angular speed
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    Re: Angular Speed and Velocity Problem

    Quote Originally Posted by Chaim View Post
    But I was wondering, when I'm converting degrees into radians, why would that be the angular speed? Just wondering, cause I checked the internet of converting degrees, but do not understand how I would know that would be the angular speed
    (degrees/sec)(pi/180) = radians/sec
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