An atwood machine consists of two masses, ma = 6.8 kg and mb = 8.0 kg , connected by a cord that passes over a pulley free to rotate about a fixed axis. the pulley is a solid cylinder of radius r0 = 0.40 m and mass 0.80 kg .1. determine the magnitude of the acceleration a of each mass.
2. what percentage of error in a would be made if the moment of inertia of the pulley were ignored? ignore friction in the pulley bearings.

To solve this problem it is necessary to apply the concewptos related to Torque, kinetic movement and Newton's second Law.

By definition Newton's second law is described as

F= ma

Where,

m= mass

a = Acceleration

Part A) According to the information (and as can be seen in the attached graph) a sum of forces is carried out in mass B, it is obtained that,

In the case of mass A,

Making summation of Torques in the Pulley we have to

Replacing the values previously found,

Replacing with our values

PART B) Ignoring the moment of inertia the acceleration would be given by

Therefore the error would be,