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sergiokapone
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Homework Statement
Rotating with angular velocity ##ω_0## solid homogeneous cylinder of radius ##r## placed without starting forward speed at the bottom of the inclined plane, forming an angle ##\alpha## with the horizontal plane, and starts to roll in up. Determine the time during which the cylinder reaches the highest position on the inclined plane.
Homework Equations
##m\dfrac{dv}{dt}=F-mg\sin\alpha##
##I\dfrac{d\omega}{dt}=Fr##
The Attempt at a Solution
From integrating of the above eqns, I get:
##\dfrac{\omega r}{2}-v=g\sin\alpha \cdot t-const##
Where the constant we can determine from the initial conditions, e.g.
##const=-\dfrac{mr\omega_0}{2}##
So, I get eqn
##\dfrac{\omega r}{2}-v=g\sin\alpha \cdot t-\dfrac{\omega_0 r}{2}##
I think that at the start of pure rotation, the cylinder has to stop, ie, it reaches the maximum height. How is it possible to argue?
Then ##v=-\omega r##, and ##\omega=0##
##0=g\sin\alpha \cdot t-\dfrac{\omega_0 r}{2}##
##t=\dfrac{\omega_0 r}{2g\sin\alpha}##
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