physics

A clothes dryer is spinning at 75 rpm. A student opens its door and it comes to rest after rotating through four revolutions. Assume constant deceleration. What was the magnitude of the dryer's angular deceleration?

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  1. Vi = 75 * 2 pi radians/min *1 min/60 sec
    = 5 pi/2 radians/second

    v = Vi - a t
    0 = 5 pi/2 - a t
    so t = 5 pi/2a

    4*2pi = Vi t + (1/2) a t^2

    8 pi = ( 5 pi/2)(5 pi/2a) + (1/2)a (5 pi/2a)^2

    etc

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  2. Vi = 75 * 2 pi radians/min *1 min/60 sec
    = 5 pi/2 radians/second

    v = Vi - a t
    0 = 5 pi/2 - a t
    so t = 5 pi/2a
    +++++++++ a is assumed negative +++
    4*2pi = Vi t - (1/2) a t^2

    8 pi = ( 5 pi/2)(5 pi/2a) - (1/2)a (5 pi/2a)^2

    8 pi a = (5 pi/2)^2 = (1/2)(5 pi/2)^2

    8 pi a = (1/2)(5 pi/2)^2
    16 pi a = 25 pi^2/4
    a = (25/64) pi
    remember it is negative (deacceleration)

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