FYKOS Year 30 Series 3 Problem 5 — pulleying · FYKOS 30 #30.3.5

Physics · mechanics

Problem

Consider the pulley system in the picture. If the masses

m_{i}

, radii

R_{i}

, and moments of inertia

J_{i}

for all pulleys, mass

m

of the weight, and mass

M

, radius

R

, and moment of inertia

J

of the cylinder are all known, we neglect the weight of pulley 2 and thus consider the ropes leading to pulley 2 as parallel with the inclined plane, the coefficient of friction (both static and kinetic) between the cylinder and the surface is

f

and the rope does not slip on the pulleys, determine the acceleration (optionally the angular acceleration as well) of the weight

m

and the cylinder

M

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