Understanding Moment of Inertia in a Rotational System

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SUMMARY

The discussion focuses on calculating the moment of inertia for a rotational system involving two blocks and a rigid rod. The masses m1 = 5 kg and m2 = 15 kg are suspended from a 1.5 m rod, which has a moment of inertia I(com) = ML^2/12 about its center of mass. The key conclusion is that the masses should not be included in the moment of inertia calculation when they are not rigidly attached to the rod, as clarified by the teacher. This distinction is critical for accurate calculations in rotational dynamics.

PREREQUISITES
  • Understanding of moment of inertia and its calculation.
  • Familiarity with rotational dynamics and Newton's laws.
  • Knowledge of rigid body motion and point mass approximation.
  • Basic trigonometry for angle calculations in rotational systems.
NEXT STEPS
  • Study the concept of rigid body dynamics in detail.
  • Learn about the parallel axis theorem for moment of inertia calculations.
  • Explore examples of rotational motion involving multiple masses.
  • Review the differences between point masses and rigidly attached bodies in physics problems.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and rotational dynamics, as well as educators seeking to clarify concepts related to moment of inertia and rigid body motion.

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Homework Statement


hello everyone ,, can someone tell me if I got the moment of inertia right or wrong of this question :
Two blocks of masses m1 = 5 kg and m2 = 15 kg are suspended from the ends of 1.5 m
rigid rod of weight 75 N that can rotate about point P, as shown in the figure. The rod is
held in a configuration such that it makes an angle of 37° with the vertical, and then
released. The two blocks can be considered as point particles and the moment of inertia
of the rod about its center of mass is I(com) = ML^2/12.


Homework Equations





The Attempt at a Solution


I=I(com)+M(L/3)^2+m1(2L/3)^2+m2(L/3)^2 = (7/36)ML^2+(m2L^2/9)+(4m1L^2/9),, my teacher told me that adding m2 and m1 is wrong ,, but what i don't get ,, in some questions we add them ,, so is he right or wrong ??
 

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And the figure shows what exactly?
 
Attach the figure.
 
sorry ,, forgot to add it
 
The masses are not rigidly attached to the stick, so don't include them when calculating the rotational inertia.
 
how come we don't include them ?? in the previous question (https://www.physicsforums.com/showthread.php?t=314630) we added them to the moment of inertia ,, in Fundamentals of physics book there is a question in Rotation chapter (11) Q:57P ,, in the answer .. it I*Alfa = (mL^2(1)+ mL^2(2))*alfa and it's almost the same as the question but without angle (it's horizontal) but I equaled : (mL^2(1)+ mL^2(2)) (the rod is mass less in this question)
By rigidly ,, you mean it fixed and can't be taken away ? ,, BTW some questions say (without the cord slipping on the pulley) does it mean it fixed ?
 
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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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