A box attached to a Massive Pulley

physics simulation

Instructions: Click Go to release the mass. Use the sliders to adjust the masses of the two components.
Explanation: This simulation shows a classic example from rotational kinematics. Assuming the moment of inertia of the pulley is $$ I = M R^2$$ where $M$ is the mass of the pulley and $R$ is its radius ($R = 1$ for this example), we can solve the equations of motion to find the acceleration of box of mass $m$ to be $$a = g \left(\frac{2m}{2m+M} \right)$$ in terms of $g$. Notice that if the mass of the pulley is zero $M = 0$, the acceleration simply reduces to $g$, the acceleration of a free mass.

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moment of inertia

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