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Tyre rotation

  1. Sep 29, 2009 #1
    1. The problem statement, all variables and given/known data
    A bicycle is rolling down a circular hill that has a radius of 9.00m. The angular displacement of the bike is 0.960rad. The radius of each wheel is 0.400m. What is the angle (in radians) through which each tyre rotates ?


    Notes on question :
    - wheels are in rolling motion (involves rotation)
    - bicycle speed and wheel speed is angular


    2. Relevant equations
    angle = 1/2 (Wo + W)t
    angle = WoT + 1/2(angular displacement)Tsquared



    3. The attempt at a solution
    From theoretical point, would jus like to know how to aproach the question as the only given data is displacement and length. If I could calcualte 2 more variables I can use a kinematics equation.
     
  2. jcsd
  3. Sep 29, 2009 #2

    Redbelly98

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    Welcome to PF :smile:

    I don't understand the situation being described. In particular, what does this mean:

    The angular displacement of the bike is 0.960rad.​

    Does this refer to the bike's position on the circular hill? If so, does a displacement of 0rad correspond to the top or bottom of the hill, or somewhere else? Is the hill itself a full circle, a semicircle, or some other portion of a circle?

    I suspect the key is to figure out over what distance the bike travels. Angular velocities and accelerations don't seem to play a role here.
     
  4. Sep 30, 2009 #3
    Thanx for the welcome

    The angular displacement refers to the distance the bicycle has travelled on the circular path.

    The hill could be imagined be a circle. I tried to approach the question from a rolling motion point of view, whereas the linear speed and angular speed has a relation, but seeing that the bike is not traveling on a straight line it's not the rite way.

    Doesnt the bike's angular displacement relate to the wheel's angle ? Seeing that both object are rotating around a fixed axis
     

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  5. Sep 30, 2009 #4

    Redbelly98

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    I can't see your figure yet, but it sounds like you'll need the arc-length formula. That's the formula which relates arc-length, radius, and angular displacement for a circle.
     
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