December 12th, 2016, 11:38 AM  #1 
Newbie Joined: Dec 2016 From: United States Posts: 2 Thanks: 0  Linear and Angular Speed?
A wheel of radius 10 inches is rotating 30°/sec. What is the linear speed in in/sec and the angular speed in RPM? What is the angular speed in radians/sec?

December 12th, 2016, 12:10 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,426 Thanks: 1195 
linear speed is $v = r\omega$ where $v$ is in in/sec, $r$ is in inches, and $\omega$ is in radians/sec start by converting 30 deg/sec to radians/sec to convert rad/sec to RPM (rev/min) ... $\dfrac{radians}{sec} \cdot \dfrac{1 \, revolution}{2\pi \, radians} \cdot \dfrac{60 \, sec}{1 \, min} = \dfrac{rev}{min}$ 
December 12th, 2016, 10:42 PM  #3  
Member Joined: Oct 2016 From: labenon Posts: 33 Thanks: 4  Linear and Angular speed? Quote:
Or you can use this formula: Linear speed = Angular speed x Radius of the rotation v = ωr v = linear speed (m/s) ω = angular speed (radians/s) r = radius of the rotation (m)  

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