"The flywheel rotates with angular velocity of w=0.005theta^2 rad/s. Determine the angular acceleration after it has rotated 20 revolutions.
I thought the equations were all but self-evident using the problem description! (See below.)
The Attempt at a Solution
The angular velocity is merely a=0.01theta. I just plugged in 20*2pi for the acceleration at that time and was... wrong. Massively wrong, in fact. The book solutions agrees with me about my equations for w and a, but they actually multiple the acceleration and the velocity together!
The book defines alpha as dw/dtheta... but then, in this solution set, states that alpha=w(dw)(dtheta), which is not something I can make *any* sense out of. They then use this value of alpha to compute the acceleration over a rotation of (40pi), complete with theta cubed.
What happened here? I can't make heads or tails of it.