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Math Help - Bike and Sprocket problem

  1. #1
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    Bike and Sprocket problem

    You are riding a bike along a level road. Assume each wheel is 28 inches in diameter, the rear sprocket has radius 3 inches and the front sprocket has radius r inches. Suppose you are pedaling the front sprocket at the rate of 1.5 rev/sec and your forward speed is 11 mph on the bike. What is the radius of the front sprocket?

    Answer: 4.4 inches

    So here are the key information:
    Wheel is 28 inches in diameter
    Rear sprocket has raidus 3 inches
    Front sprocket has raidus r inches
    Pedaling front sprocket at the rate of 1.5 rev/sec
    Forward speed is 11 mph
    Find raidus of front sprocket

    I'm having trouble putting all this information in my head, can anyone help me through with the steps?
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  2. #2
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    skeeter's Avatar
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    Re: Bike and Sprocket problem

    formula required ...

    v = r \omega

    v is linear speed

    r is radius

    \omega is angular speed in radians per unit time

    first, a unit conversion ...

    11 mph = (968/5) in/sec

    since v = r \omega ...


    968/5 = 14 \omega

    \omega = (484/35) radians/sec

    angular speed of the rear wheel = angular speed of the rear sprocket

    484/35 = (linear speed of the rear sprocket)/3

    linear speed of the rear sprocket = (1452/35) in/sec = linear speed of the chain connecting the front and rear sprockets.

    now you know the linear speed of the front sprocket. convert the angular speed of the front sprocket from rev/sec to rad/sec and calculate its radius.
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  3. #3
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    Re: Bike and Sprocket problem

    Quote Originally Posted by Chaim View Post
    You are riding a bike along a level road. Assume each wheel is 28 inches in diameter, the rear sprocket has radius 3 inches and the front sprocket has radius r inches. Suppose you are pedaling the front sprocket at the rate of 1.5 rev/sec and your forward speed is 11 mph on the bike. What is the radius of the front sprocket?

    Answer: 4.4 inches

    So here are the key information:
    Wheel is 28 inches in diameter
    Rear sprocket has raidus 3 inches
    Front sprocket has raidus r inches
    Pedaling front sprocket at the rate of 1.5 rev/sec
    Forward speed is 11 mph
    Find raidus of front sprocket

    I'm having trouble putting all this information in my head, can anyone help me through with the steps?
    How about looking here: Bike and Sprocket Problem
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  4. #4
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    Re: Bike and Sprocket problem

    The intent may have been to find the pedal sprocket size given the 3 in drive sprocket size but as worded the problem is flawed
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