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Math Help - Motion on a Circle

  1. #1
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    Motion on a Circle

    An object is traveling around a circle with a radius of 2 meters. If in 20 seconds the object travels 5 meters, what is its angular speed? What is its linear speed?

    Also: What is the basic difference between angular and linear speed?
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  2. #2
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    Quote Originally Posted by magentarita View Post
    An object is traveling around a circle with a radius of 2 meters. If in 20 seconds the object travels 5 meters, what is its angular speed? What is its linear speed?

    Also: What is the basic difference between angular and linear speed?
    The linear speed:
    v = \frac{d}{t}

    Where:
    • v = Linear speed
    • d = Distance travelled
    • t = Time (in which the distance is travelled)


    v = \frac{d}{t}
    v = \frac{5}{20}
    v = \frac14\text{ ms}^{-1}

    __________________
    Angular speed:
    v = r\omega

    Where:
    • v = Linear speed
    • r = Radius
    • \omega = Angular speed (In radian)


    v = r\omega
    \frac14 = 2 \omega
    \omega = \left(\frac14\right) \div 2
    \omega = \frac18\text{ rads}^{-1}

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    The Difference:
    Linear velocity is a change of speed in a straight line. Angular speed is the rate of change of angle with respect to time. These two are convertible in a case of a circle motion. In a circle, across a tangent, linear speed can be measured and across the arc traveled, angular speed can be measured.
    Last edited by Simplicity; August 15th 2008 at 07:47 AM. Reason: Presentation/Latex Correction
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  3. #3
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    Great

    A wonderful explanation!
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