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mhz
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Homework Statement
This isn't a specific question, more of a general one:
Suppose there is a cylinder of mass [itex]m[/itex] that is rotating in the positive clockwise direction with initial rotational velocity [itex]\omega_0[/itex], and radius [itex]R[/itex].
Then, suppose this rotating cylinder is placed on a surface with coefficient of kinetic friction [itex]\mu_k[/itex].
How long after it is placed this surface does it begin to roll without slipping?
Homework Equations
[itex]\tau = I\alpha \\
F = ma \\
I_{cyl} = \frac{mR^2}{2} \\
v = v_0 + at \\
\omega = \omega_0 + \alpha t \\[/itex]
The Attempt at a Solution
I'm torn between two approaches.
The first - couldn't I simply solve for a and alpha, set the two linear/angular velocity equations equal to each other for the case that v = r(omega) and solve for t?
The second - using energy, I could say that the initial rotational kinetic energy equals the final rotational kinetic energy plus toe final kinetic energy plus the energy lost to friction, find d or final velocity when v = r(omega) and use kinematics to solve for t?