Load being raised and accelerating

Torque T= T_f + Ib + mR(a + g)

Where b = a/R

Load rising and coming to rest, no drive

T_f - lb =mR(d -g)

Deceleration d = [mgR + T_f ] / [ mR + (I/R) ]

Load being lowered and accelerating, no drive

T_f + lb = mR(g -a)

Accelaration b = [mgR - T_f ] / [ mR + (I/R)]

Load falling and being brought to rest

T=Ib- T_f +mR(g +d)

Where:

Symbols used:
m = mass of load
I = moment of inertia of drum, etc.
R = drum radius
T = torque to drive drum
T_f = friction torque
a = acceleration of load
d = deceleration of load
b = angular acceleration/deceleration
g = gravity