Angular Acceleration Using Work and Energy Principals

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Discussion Overview

The discussion revolves around a homework problem involving the calculation of the initial vertical acceleration of a steel block being lifted by a crane. The problem incorporates concepts from work and energy principles, as well as angular and linear momentum.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • The initial problem statement includes specific parameters such as the mass of the chain, the radius of the drum, and the torque applied.
  • One participant suggests that the solution should involve angular and linear momentum, indicating a potential misunderstanding of the concepts involved.
  • Another participant clarifies that the sum of moments should be equated to the moment of inertia multiplied by the angular acceleration, correcting the earlier claim about angular momentum.
  • A later reply indicates that the original poster has resolved their issue, suggesting some level of understanding was achieved.

Areas of Agreement / Disagreement

There is no clear consensus on the correct approach initially, as participants express different understandings of the relationship between moments and angular momentum. However, the clarification provided seems to have helped the original poster find a solution.

Contextual Notes

The discussion does not fully explore the implications of the equations presented or the assumptions behind the calculations, leaving some mathematical steps and dependencies on definitions unresolved.

Who May Find This Useful

This discussion may be useful for students working on similar physics problems involving torque, angular acceleration, and the application of work and energy principles in mechanical systems.

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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

 

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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
 
Sum of moments is not angular momentum. Sum of moments is the moment of inertia multiplied by the angular acceleration.
 
I solved it many thanks for your help.
 

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