Equations For A Pulley With Inertia and Friction
For very small mass differences between m1 and m2, the rotational inertia I of the pulley of radius r cannot be neglected. The angular acceleration of the pulley is given by the no-slip condition:
where is the angular acceleration. The net torque is then:
Combining with Newton's second law for the hanging masses, and solving for T1, T2, and a, we get:
Acceleration:
Tension in string segment nearest m1:
Tension in string segment nearest m2:
Should bearing friction be negligible (but not the inertia of the pulley and not the traction of the string on the pulley rim), these equations simplify as the following results:
Acceleration:
Tension in string segment nearest m1:
Tension in string segment nearest m2:
Read more about this topic: Atwood Machine
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