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Math Help - Radian Measure

  1. #1
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    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!
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  2. #2
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    Re: Radian Measure

    v = r\omega

    \frac{\9.6\pi}{10} \, m/s = r (1.2\pi \, rad/s)
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  3. #3
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    Re: Radian Measure

    Quote Originally Posted by misiaizeska View Post
    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 \theta is L=r\theta.
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  4. #4
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    Re: Radian Measure

    I presume you know that circumference of a circle of radius r is 2\pi r. That divides into 9.6\pi 4.8/r times so the wheel must have turned through 4.8/r revolutions. Since each revolution is 2\pi radians, that will be (4.8/r)(2\pi)= (9.6/r)\pi radians. Since we are told that the wheel turned at 1.2\pi radians per second for 10 seconds, it actually turned through 12 radians: 9.6/r= 12. Solve that for r.
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  5. #5
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    Re: Radian Measure

    I used this formula - thanks to everyone!
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