1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    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

    Attached Files:

  5. Sep 30, 2009 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook