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Thread: Help with Radian Measure

  1. #1
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    Exclamation Help with Radian Measure

    A belt connects pulleys of diameter 2r and 2R with centres x apart. If r=20mm, R=120mm, and x=100*21/2mm, find the length L of the belt and the area of the region it encloses. Find the general expression for L in terms of r, R, x and Ų
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  2. #2
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    Re: Help with Radian Measure

    Sketch attached to help you get started ...
    Attached Thumbnails Attached Thumbnails Help with Radian Measure-belt_prob.png  
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    Re: Help with Radian Measure

    Yes, from that diagram I was able to work out that:
    cosŲ=100/100sqrt2
    i.e.Ų=pi/4

    But from that how do you work out the length of the belt?
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    Re: Help with Radian Measure

    Quote Originally Posted by KiaraG16 View Post
    Yes, from that diagram I was able to work out that:
    cosŲ=100/100sqrt2
    i.e.Ų=pi/4???? But from that how do you work out the length of the belt?
    The non-blue part of the pulley's path is $\frac{3}{4}$ of the length circumference of the large circle.

    The length of the linear blue part is $20+20=40$.
    The length along the small circle is $\frac{1}{4}$ of its circumference.

    In both cases the central angle is a right angle.

    ADD these three lengths to get a total.
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