Forces (moment of inertia) Question

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SUMMARY

The discussion centers on calculating the moment of inertia and angular acceleration of a pulley system involving two blocks. The moment of inertia for the pulley is given by the formula I(com) = 0.5 * M * R^2, where M is the mass of the pulley and R is its radius. The participants clarify that the tensions in the strings and the angular acceleration can be determined using the equation TbR1 - TaR2 = I(com) * α, where α is the angular acceleration. The importance of treating the pulley and blocks as separate entities in the calculations is emphasized.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with rotational dynamics and moment of inertia
  • Knowledge of tension in strings and forces in pulley systems
  • Basic algebra for solving equations
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  • Study the derivation of the moment of inertia for different shapes, particularly cylinders and disks
  • Learn about angular acceleration and its relationship to linear acceleration in pulley systems
  • Explore the principles of tension in multi-block pulley systems
  • Review examples of rotational dynamics problems to reinforce understanding
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Students studying physics, particularly those focusing on mechanics and rotational dynamics, as well as educators looking to clarify concepts related to moment of inertia and pulley systems.

Lord Dark
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Homework Statement


hi everyone,, I need an explanation for this question:
A 1.0 kg block A is hanged by a light string from a pulley of mass
M = 1.0 kg. Another block B of mass 4.0 kg is attached to a mass-less rope wound around a mass-less shaft. The pulley has a radius 260.0 Rcm= and the shaft has a radius. The block B is released from rest when it is at height h = 4.0 m above the ground. 130.0 cm R=
The rotational inertia (moment of inertia) of the pulley with respect to its center of mass is.
I(com)=0.5*M*R2^2

(a) Find the angular acceleration of the pulley.
(b) Find the accelerations of the blocks.
(c) Determine the tensions in the strings.
(d) Find the speeds of the block A and block B just before the block B hits the ground.

Homework Equations


The Attempt at a Solution


Actually ,, I have the answer ,, but the problem I don't know how did he get the moment of inertia like that (in the attachment)
 

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Lord Dark said:
Actually ,, I have the answer ,, but the problem I don't know how did he get the moment of inertia like that (in the attachment)
You have the mass of the pulley and are told the equation to use to find its moment of inertia. Maybe you can restate your question.
 
I mean shouldn't I=I(com)+M1R1^2+M2R2^2 ??
 
Lord Dark said:
I mean shouldn't I=I(com)+M1R1^2+M2R2^2 ??
No, those masses are not rigidly attached to the pulley. The only thing rotating here is the pulley. Treat this as three separate objects: m1, m2, and m3.
 
then the teacher's answer is wrong ? and TbR1-TaR2=I(com)*alfa only ?? not like his answer ? (in the attachment)
 
Lord Dark said:
then the teacher's answer is wrong ? and TbR1-TaR2=I(com)*alfa only ?? not like his answer ? (in the attachment)
What makes you think that the teacher is doing anything other than TbR1-TaR2=I(com)*alfa? (Where I is just the rotational inertia of the pulley.) That's his equation #3.

(You could lump them all together, but I would not advise it. Do it like your teacher did. Write three separate equations, then combine them.)
 
aha ,, now I get it :) ,, actually I didn't focus on what he wrote ,, thanks again ,, am bothering you this day (my last day :D)
 

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