Trigonometry

a bicycle with 24inch diameter wheels is traveling at 15mi/hr.
a) Find the angular speed of the wheels in rad/min.
b)How many revolutions per minute do the wheels make?

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  1. Diameter = 24 in
    Radius = 12 in

    (a) angular speed (ω) = ?
    We use the formula:
    v = ω r
    Substituting,
    15 mi/hr = ω * 12 in
    Note that 1 mile = 63360 inches, and 1 hour = 60 min:
    15 mi * (63360 in / mi) / (1 hr * 60 min / hr) = ω * 12 in
    15840 in / min = ω * 12 in
    ω = 15840 / 12
    ω = 1320 rad/min

    (b) rev/min = ?
    Note that 1 revolution = 2π. Thus,
    1320 rad/min * 1 rev / 2π rad = 210.08 rev/min

    hope this helps~ `u`

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  2. Thank you Jai!

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