How do I calculate the minimum torque to rotate a .925lb, 0.625' diameter shaft with a .925lb 2.19' hub 10K rpm within 3 seconds? I am trying to spec out an electric motor that I can couple up to the shaft supported by two ball bearings to spin test the hub on.

T=IxA

"I" inertia for a solid shaft, I=1/2MR^2 = 1/2*0.925lb * (1.095in)^2 = 0.55 lb-in^2

"R" - radius = (2.19in/2)= 1.095in

"M" - mass = 0.925 lb

"A" assume to use Angular Acceleration, A= 10,000 rpm * 2pi * 1/60 sec = 1047 rad/sec

T = 0.55 lb-in^2 * 1047 rad/sec * 3 seconds = 1727.55 lb-in^2 This is where it does not makes sense, because I know T units british units if lb-in. How do I get rid of one of the "in" units? Where did I go wrong?

Thanks.