# Rotational Motion: System Tip

Submitted by zAev7C2WHP in Physics (edited )

assume an object is on a frictionless table connected by a string with negligable mass, through a pulley with mass (no friction), and finally connected to another object suspended in the air: https://coinsh.red/p/download.png

to find the acceleration of the system net a = net f / net m

Latex: \sum\nolimits a = \sum\nolimits F / \sum\nolimits M

Now, this answer would be simple if the pulley were considered a point mass with rotational inertia of MR^2, but most are considered to be a disk, leaving a rotational inertia of .5MR^2

The change in the rotational inertia affects the equation:

Latex: \sum\nolimits a = Mg / (m_{1} + M_{2} + km_{p})

where k is a constant directly related to kMR^2

tl;dr mass of the pulley isn't directly mass into the system

I used http://quicklatex.com/ for the latex parts.