physics

A bicycle is rolling down a circular portion of a path; this portion of the path has a radius of 8.73 m. As the drawing illustrates, the angular displacement of the bicycle is θ = 0.979 rad. What is the angle (in radians) through which each bicycle wheel
(radius = 0.320 m)
rotates?
s=0.979*8.73=8.55m
angle in rad=8.55/0.320=26.71

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  1. .979 * 8.73 = 8.55 meters along the path

    .32 theta = 8.55
    so
    theta = 26.7 rad
    yes

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  2. This will help you get to the correct answer: This is what Wiley gave for the Tutorial hints

    (a) Based on the drawing, what is the circular arc length traveled by the axle of the wheel?

    The circular arc length traveled by the axle of the wheel is equal to the angular displacement θ, multiplied by the radius of the path minus the radius of the wheel.

    From elementary geometry, the arc length is equal to the angle multiplied by the radius. The radius of the arc that the axle travels is equal to the radius of the path minus the wheel’s radius. Therefore, the arc length traveled by the axle is just the angular displacement multiplied by the radius of the path minus the radius of the wheel.

    So essentially what you do is this:

    1.) S = theta x (radius of path- radius of wheel) = the displacement travelled by the axle of the wheel

    2.) Angle in radians: theta = S (displacement above) / radius of bike

    Hope this helps!

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