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Math Help - linear speed and centripetal acceleration

  1. #1
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    linear speed and centripetal acceleration

    The front and rear sprockets on a bicycle have radii of 9.00 and 5.10 cm, respectively. The angular speed of the front sprocket is 6.00 rad/s. Determine the following.
    (a) The linear speed of the chain as it moves between the sprockets.
    cm/s

    (b) The centripetal acceleration of the chain as it passes around the rear sprocket.
    cm/s2


    i think the formula is something like: sqrt(r^2 * w^4 + r^2((w-w0)/t)^2)

    however, there are two radius' ?

    also, not sure how to compute the speed.
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  2. #2
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    Quote Originally Posted by rcmango View Post
    The front and rear sprockets on a bicycle have radii of 9.00 and 5.10 cm, respectively. The angular speed of the front sprocket is 6.00 rad/s. Determine the following.
    (a) The linear speed of the chain as it moves between the sprockets.
    cm/s
    The chain can only move at one linear speed over either sprocket. So we know the radius and angular speed of the front sprocket, thus
    v = r_f \omega _f
    (where the subscript "f" repesents the front sprocket.)

    Quote Originally Posted by rcmango View Post
    (b) The centripetal acceleration of the chain as it passes around the rear sprocket.
    cm/s2
    We now know the linear speed of the chain so we can calculate the angular speed of the rear sprocket:
    v = r_r \omega _r

    \omega _r = \frac{v}{r_r}

    Now we can calculate the centripetal acceleration of the chain as it goes around the rear sprocket:
    a_c = r \omega ^2

    Hint: Stick to the basics when problem solving. I don't even recognize that formula you posted.

    -Dan
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