trigonometry

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A truck with 48-in.-diameter wheels is traveling at 45 mi/h.
(a) Find the angular speed of the wheels in rad/min.
rad/min

(b) How many revolutions per minute do the wheels make?
rev/min

  • trigonometry -

    one rotation = 2π(48) = 96π inches

    in 1 hour it goes 45 miles
    = 45x5280x12 inches
    = 2851200 inches

    number of rotations per hour
    = 2851200/(96π) = 9453.8.. rotations per hour
    = 157.563 rpm

    = 157.563x(2π) radians /min
    = 990 radians/min

  • trigonometry -

    45 mi/hr * 5280*12 in/mi /(2pi*48in/rev) * hr/60min * 2pi rad/rev = 3960 rev/min

    rev/min = rad/min * rev/2pi rad, so divide 3960 by 2pi

  • trigonometry -

    Oops. Off by a factor of 2. I was using a radius of 48 in

  • trigonometry -

    Rats, I read it wrong also
    radius should have been 24 , not 48

    make the necessary adjustments in the above.

    (time to go to bed)

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