Question

a flywheel of diameter 37.5 cm starts from rest and accelerates to an angular velocity of 900 rpm in 5.38 seconds. find the magnitude of the total acceleration at 1.62 seconds.

Answer #1

Diameter d = 37.5 cm = 0.375 m

Radius r = d/ 2

= 0.1875 m

Initial angular speed w = 0

Angular speed after 5.38 s is w ' = 900 rpm

= 900 x2(pi) rad / 60 s

= 94.24 rad/s

time t = 5.38 s

Angular accleration = (w ' - w ) / t

= 94.24 / 5.38

= 17.51 rad/s ^{2}

Angular speed at 1.62 s is w " = w + t '

w " = 0 +(17.51)(1.62)

= 28.37 rad/s

Centripetal acceleration a ' = rw" ^{2} =
(0.1875)(28.37) ^{2}

= 151 m/s ^{2}

Tangential accleration a = r

= 0.1875 x 17.51

= 3.283 m/s ^{2}

the magnitude of the total acceleration at 1.62 seconds =
[a
^{2} + a' ^{2}]

= 151.03 m/s ^{2}

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