Angular Acceleration Using Work and Energy Principals

[mm391]

Homework Statement

The chain of a workshop crane is 50 m long and has a mass of 3 kg/m. It is partially wound on a drum and the effective radius from the axis of the drum to the chain centre line is 0.2 m. The drum itself, including shaft and gear wheel has a mass of 100 kg and has a radius of gyration of 0.15 m. A steel block with a mass of 500 kg is to be lifted from a point 20 m below the level of the axis of the drum. If a torque of 1.3 kNm is applied to the drum, what will be the initial vertical acceleration of the steel block?

Homework Equations

P.E = mgh
K.E = 1/2mv^2
I = mK^2
Torque = radius * Force
Work Done = F*distance
F=mass* acceleration

The Attempt at a Solution

 

[mm391]

I have just found out it is meant to be using angular and linear momentum but I a m still stuck:

Sum of moments = angular momentum

Momentum = Inertia*angular velocity + mass*velocity*radius

 

[LawrenceC]

Sum of moments is not angular momentum. Sum of moments is the moment of inertia multiplied by the angular acceleration.

 

[mm391]

I solved it many thanks for your help.