Answer to Question #152407 in Classical Mechanics for Greyfia

Question

Two pulleys with masses m1 = 1 (kg) and m2 = 2 (kg) fixed
coaxially to each other are fixed on the wall so that they can rotate around point O (bigger pulley has 2r and the small one on the inside of the big one has radius r). Mass m3 = 3 (kg) is connected to the rope wound on a reel with radius r = 1 (m). Initially a constant force of

Answer 1

Moment of inertia of system can be written as

$I=\frac{1}{2}m_1(2r) ^2+\frac{1}{2}m_2r^2$

By putting value

$I=\frac{1}{2}(1)(2r) ^2+\frac{1}{2}(2)r^2\\I=3r^2$