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A flywheel with initial angular velocity ω0 decelerates due to the forces whose moment relative to the axis is proportional to the square root of its angular velocity. Find the mean angular velocity of the flywheel averaged over the total deceleration time.
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1 Answers
1as we know that
torque = - Icm alpha(as it is decelerating)
Icm = MR2/2(as it is a disc)
and torque = k√w
and alpha=dw/dt
hence we get
∫dw/√w=∫2k/MR2dt
first inetgrate it left = w0 to w(at any point of time)
and the right from 0 to t
u will get w as a function of T = (i)
what you have to find is
mean value of w
=0∫Twdt/T
T = time required to stop (which you can get by putting w=0 in (i) and calculating T)
and as you already have w as a function of t
you can do the above integration
the answer will come out to be =w0/3