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A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 10 rev/s; 60 revolutions later, its angular speed is 15 rev/s. Calculate

(a) the angular acceleration,
(b) the time required to complete the 60 revolutions,
(c) the time required to reach the 10 rev/s angular speed, and
(d) the number of revolutions from rest until the time the disk reaches the 10 rev/s angular speed.

User Curly
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1 Answer

3 votes

Step-by-step explanation:

Given:


\omega_0 = 10 rev/s =
20\pi\:\text{rad/s}


\omega = 15 rev/s =
30\pi\:\text{rad/s}


\theta = 60 rev =
120\pi\:\text{rads}

a) the angular acceleration
\alpha is given by


\alpha = (\omega^2 - \omega_0^2)/(2\theta)


\:\:\:\:\:\:\:=((30\pi)^2 - (20\pi)^2)/(240\pi) = 6.5\:\text{rad/s}^2

b)
t = (\omega - \omega_0)/(\alpha) = (30\pi - 20\pi)/(6.5) = 4.8\:\text{s}

c)
t = (\omega - \omega_0)/(\alpha)


=(20\pi - 0)/(6.5) = 9.7\:\text{s}

d)
\theta = (1)/(2)\alpha t^2


\:\:\:\:\:\:\:=(1)/(2)(6.5\:\text{rad/s}^2)(9.7\:\text{s})^2 = 305.8\:\text{rad}


\:\:\:\:\:\:\:= 48.7\:\text{revs}

User Eduardo Pedroso
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