Unraveling the Mystery of Rotational Motion and Moment of Inertia

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SUMMARY

The discussion centers on the definition of moment of inertia in the context of rotational motion of rigid bodies. A participant questions why moment of inertia is defined using the radius squared rather than the radius itself, suggesting that this could eliminate the need for torque in the equation F=I*α. However, another participant clarifies that moment of inertia is a defined term and that changing its definition based on a single case oversimplifies the broader principles of physics, similar to the constants used in Coulomb's law.

PREREQUISITES
  • Understanding of rotational motion concepts
  • Familiarity with moment of inertia and its mathematical representation
  • Knowledge of torque and its role in rotational dynamics
  • Basic grasp of Coulomb's law in electrostatics
NEXT STEPS
  • Research the mathematical derivation of moment of inertia for various shapes
  • Explore the relationship between torque and angular acceleration in rigid body dynamics
  • Study the applications of moment of inertia in real-world engineering problems
  • Investigate the significance of constants in physical laws, such as ε0 in electrostatics
USEFUL FOR

Students of physics, educators teaching rotational dynamics, and engineers involved in mechanical design will benefit from this discussion.

AmonRaMAsr
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This a question that has been haunting me for some time now. Regarding the rotational motion of rigid bodies why wasn't the moment of inertia defined as the integral sum elements of infinitesimal mass time the radius from the axis of rotation rather than the radius squared. In this case the equation would look something like this.
F=I*\alpha
and their would be no need for introducing the concept of the torque.
thnx in advance
 
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AmonRaMAsr said:
This a question that has been haunting me for some time now. Regarding the rotational motion of rigid bodies why wasn't the moment of inertia defined as the integral sum elements of infinitesimal mass time the radius from the axis of rotation rather than the radius squared. In this case the equation would look something like this.
F=I*\alpha
and their would be no need for introducing the concept of the torque.
thnx in advance

well, a good question. but it is a question not to be asked...first moment of inertia is a definition and definitions can't be put to questions...second you can't just consider one case to change a definition (just like you said it simplifies force eq)...for ex if you are done with the coulumb's law of electrostatics the value of constant is often written as 1/ 4 * pi *\epsilon0...in which all are constants...have you ever thought why coudnt they call an entire thing as a new constant instead of interducing a new constant \epsilon0..this is because that \epsilon0 is useful in many other places (like gauss law)...
 

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