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Considering a pulley with some mass, or some friction, How can its inertia (or momentum of inertia) influence the tension on 1 rope? Which part of the rope is influenced? Before or after the pulley?

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  • $\begingroup$ You can find out if you plot free body diagram for pulley and rope separately. $\endgroup$ – lucas Apr 22 '16 at 19:20
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The important thing is the difference in tension between the ropes on either side of the pulley.

So you will have $(T_2-T_1) R = I_{\text {pulley}}\alpha$ where $T_1$ and $T_2$ are the tensions on either side of the pulley, $R$ is the radius of the pulley, $I_{\text {pulley}}$ the moment of inertia of the pulley and $\alpha$ the angular acceleration of the pulley.

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