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2 February, 12:54

An auto race is held on a circular track. A car completes one lap in a time of 24.6 s, with an average tangential speed of 38.0 m/s. Find (a) the average angular speed and (b) the radius of the track.

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  1. 2 February, 13:23
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    (a) 0.255 rad/s.

    (b) 149.02 m

    Explanation:

    (a)

    The expression for the average angular speed of the car is given as,

    ω = 2π/T ... Equation 1

    Where ω = Angular speed, T = period of the car, π = pie.

    Given: T = 24.6 s,

    Constant: π = 3.14

    Substitute into equation 1

    ω = 2 (3.14) / 24.6

    ω = 0.255 rad/s.

    (b)

    The expression for tangential speed, angular speed and radius s given as

    s = rω ... equation 2

    Where s = tangential speed, r = radius of the track, ω = angular speed.

    make r the subject of the equation

    r = s/ω ... Equation 3

    Given: s = 38 m/s, ω = 0.255 rad/s

    Substitute into equation 3

    r = 38/0.255

    r = 149.02 m.

    Hence the radius of the track = 149.02 m
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