Moment of Inertia: Problem 8 Homework Solutions

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SUMMARY

The discussion centers on solving Problem 8 related to the moment of inertia, with a calculated value of 4.3 kg*m². Participants debated the validity of using specific equations for velocity and acceleration in the context of a wheel assumed to be a uniform disk. The correct approach involves using the relationship between linear acceleration and angular acceleration, specifically a = rα, and applying the torque equation τ = Iα to solve for the moment of inertia directly.

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  • Understanding of moment of inertia concepts
  • Familiarity with torque equations
  • Knowledge of angular and linear acceleration relationships
  • Basic principles of rotational dynamics
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  • Learn about the relationship between linear and angular motion
  • Explore the application of torque in rotational systems
  • Investigate the assumptions made in rotational dynamics problems
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Students studying physics, particularly those focusing on mechanics and rotational dynamics, as well as educators seeking to clarify concepts related to moment of inertia.

jimbo71
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Homework Statement


see problem 8 attachment


Homework Equations


see problem 8 attempt attachment


The Attempt at a Solution


see problem 8 attempt attachment
I think I have solved the problem correctly and through my method I determine the moment of inertia to be 4.3 kg*m^2. However I'm not sure if the equations I used to find velocity and acceleration are valid in this situation.
 

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  • 1031-10871-problem 8.jpg
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  • 2899-33757-problem 8 attempt.jpg
    2899-33757-problem 8 attempt.jpg
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Hi jimbo71,

jimbo71 said:

Homework Statement


see problem 8 attachment


Homework Equations


see problem 8 attempt attachment


The Attempt at a Solution


see problem 8 attempt attachment
I think I have solved the problem correctly and through my method I determine the moment of inertia to be 4.3 kg*m^2. However I'm not sure if the equations I used to find velocity and acceleration are valid in this situation.

I think the assumption you have made (that is not necessarily true) is that the wheel is a uniform disk.

Once you found the linear acceleration of 0.75 m/s2, you can directly find the angular acceleration alpha from [itex]a=r\alpha[/itex].

Then you can use the torque equation like you did, but there is no need try to write out an expression for I, since I is what you want. Just use:

[tex] \tau = I\alpha[/tex]

and solve for I.
 

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