The moment of inertia of a loader crane with no load is 10 s

The moment of inertia of a loader crane with no load is 10 slug-ft2 about the motor y-axis. The moment of inertia of a 50 lb box load on the crane is 7.5 slug-ft2 about its centroid. What torque about the y-axis is necessary to give the crane with the 50 lb load an angular acceleration of 3 rad/s2.

Solution

1 Slug = 32.174 lb
I_crane,y = 10 slug-ft² = 321.74 lb-ft²
I_box,y = (7.5*32.174) lb-ft² + (50lb)*(6²ft²) = 2041.305 lb-ft²
I_net,y = I_crane,y + I_box,y = 2363  lb-ft² = 99.57 Kg-m²

From the relation, torque = I x angular acceleration
   torque = 99.57 Kg-m² x 3 rad/s² = 298.73 N-m