Radian Measure

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• Dec 1st 2012, 02:27 PM
misiaizeska
Radian Measure
A wheel rotating an an angular velocity of 1.2π radians/s, while a point of circumference of the wheel travels 9.6π m in 10s. What is the radius of the wheel?
I'm not really sure where to start; I know that the wheel makes 36 revolutions in one minute but I'm not sure how to find the circumference or radius. Any suggestions/hints?

I know that the answer is 0.8 m, just not sure how to calculate this.

Please and thank you!
• Dec 1st 2012, 03:45 PM
skeeter
Re: Radian Measure
$\displaystyle v = r\omega$

$\displaystyle \frac{\9.6\pi}{10} \, m/s = r (1.2\pi \, rad/s)$
• Dec 1st 2012, 03:48 PM
Plato
Re: Radian Measure
Quote:

Originally Posted by misiaizeska
A wheel rotating an an angular velocity of 1.2π radians/s, while a point of circumference of the wheel travels 9.6π m in 10s. What is the radius of the wheel?

The length of the arc subtended by an angle $\displaystyle \theta$ is $\displaystyle L=r\theta$.
• Dec 1st 2012, 05:02 PM
HallsofIvy
Re: Radian Measure
I presume you know that circumference of a circle of radius r is $\displaystyle 2\pi r$. That divides into $\displaystyle 9.6\pi$ 4.8/r times so the wheel must have turned through 4.8/r revolutions. Since each revolution is $\displaystyle 2\pi$ radians, that will be $\displaystyle (4.8/r)(2\pi)= (9.6/r)\pi$ radians. Since we are told that the wheel turned at $\displaystyle 1.2\pi$ radians per second for 10 seconds, it actually turned through 12 radians: 9.6/r= 12. Solve that for r.
• Dec 2nd 2012, 12:37 PM
misiaizeska
Re: Radian Measure
I used this formula - thanks to everyone! :)