Simple Moment of Inertia Question

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SUMMARY

The discussion centers on calculating the moment of inertia for a rod pivoted at one end with a mass (m) attached at a distance (L) from the pivot. To increase the moment of inertia by a factor of 5, the original poster proposed adding four additional masses at the same distance L. The moment of inertia is defined by the equation I = Σ(m_i * r_i²). The conversation highlights that multiple solutions exist depending on constraints such as the number of masses or their sizes.

PREREQUISITES
  • Understanding of moment of inertia and its formula I = Σ(m_i * r_i²)
  • Basic knowledge of physics concepts related to rotational motion
  • Familiarity with mass distribution and its effects on inertia
  • Ability to solve algebraic equations related to physical quantities
NEXT STEPS
  • Explore different configurations for mass distribution to achieve desired moment of inertia
  • Learn about the effects of adding masses at varying distances from the pivot
  • Investigate constraints in physics problems and their impact on solution strategies
  • Study advanced concepts in rotational dynamics, including torque and angular momentum
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Students studying physics, particularly those focusing on mechanics and rotational motion, as well as educators looking for examples of moment of inertia calculations.

tachu101
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Homework Statement


A rod of negligible mass is pivoted about one end. Masses can be attached to the rod at various positions along the rod. Currently, there is a mass (m) attached a distance (L) from the pivot. To increase the moment of inertia about the pivot by a factor of 5, you must attach...


Homework Equations



I=mr^2

The Attempt at a Solution



Io= mL^2
If= 5(Io) = mL^2(original mass)+4(mL^20) All I did was add four more masses of equal size at a distance L from the pivot. Is there another solution?
 
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You are correct. The definition of moment of Inertia is [tex]\sum_{i} m_{i} r^{2}_{i}[/tex]
 
tachu101 said:
All I did was add four more masses of equal size at a distance L from the pivot. Is there another solution?
Sure, there are plenty of solutions. The question is a bit vague. Are there any constraints given? (Such as the the number of masses you are allowed to add or the size of the masses.)

For example: What if you could only add a single mass of equal size. How could you solve the problem then?
 

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