Translational/Rotation Question (Pulley)

[dan38]

Homework Statement

Compound pulley with a mass (10kg) attached to outer drum
R = Outer Radius (250 mm)
r = Inner Radius (150 mm)

Horizontal force of 250 N being applied at edge of inner drum
Friction torque of 7 N m present
Mass of pulley = 20 kg and it has radius of gyration of 160 mm

Homework Equations

The Attempt at a Solution

I * Angular Acceleration + 10* Acceleration * R = F*r - 7

Where I = mk^2 of the pulley
and Acceleration = Angular Acceleration * R

Basically used these equations and inputted the given values, but still got the wrong answer.

 

[nilesh_pat]

I = 20* (160^2) = 512000 kg m^2512000 * Angular Acceleration + 10* Acceleration * 250 = 250* 150 - 7Acceleration = 1250000/512000 = 2.441406 rad/s^2But this answer is wrong since the answer is supposed to be 2.7 rad/s^2