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25 December, 08:45

A bicycle has wheels with a diameter of 0.630 m. It accelerates uniformly and the rate of rotation of its wheels increases from 225 rpm to 260 rpm in a time of 28.7 s. Find the linear acceleration of the bicycle.

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  1. 25 December, 09:18
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    the linear acceleration of the bicycle is 0.0403m/s²

    Explanation:

    First convert the angular given speeds to radians per second:

    ω₀ = 225rev/min * (2πrad/rev) * (1.00min/60.0sec)

    = 23.56 rad/s

    ω = 269rev/min * (2πrad/rev) * (1.00min/60.0sec)

    = 27.23 rad/s

    The angular acceleration is needed to find the tangential (linear) acceleration, it is:

    ω = ω₀ + αt

    α = (ω - ω₀) / t

    = (27.23rad/s - 23.56rad/s) / 28.7s

    = 0.128rad/s²

    The linear acceleration is:

    linear acceleration = angular acceleration * r

    a = rα

    r = d/2

    r = 0.630/2 = 0.315

    a = rα

    = (0.315m) (0.128rad/s²)

    = 0.0403m/s²

    Hence, the linear acceleration of the bicycle is 0.0403m/s²
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