Rotational Mechanics: Comparing Cylinder P & Q

AI Thread Summary
Cylinder P has a greater moment of inertia than cylinder Q because its mass is concentrated near its surface, while Q has most of its mass near the axis. The instantaneous axis of rotation for both cylinders is located at the point of contact with the inclined plane as they roll down. Both cylinders will reach the ground with the same translational kinetic energy, assuming no energy loss due to friction or air resistance. The discussion highlights the importance of mass distribution in determining rotational dynamics. Understanding these concepts is crucial for analyzing the motion of rolling objects.
joker94
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Two solid cylinders p and Q of same mass and same radius start rolling down a fixed inclinded plane from the same height at the asme time.cylinder P has most of its mass concentrated near its surface while Q HAS MOST of its mass near the axis...
THEN
1)WHICH HAS MORE MOMENT OF INERTIA AND WHY?
2)WHAT IS THE INSTANTEOUS AXIS OF ROTATION??
3)DOES BOTH CYLINDERS REACH THE GROUND WITH SAME TRANSLATIONAL KINECTIC ENERGY?
 
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hi joker94! welcome to pf! :wink:

tell us what you think, and then we'll comment! :smile:​
 
hi...can we consider P as a hollow cylinder then moment of inertia about the axis(which is passing through its centre) would be MR^2...AND THEN WE CAN CONSIDER Q AS A SOLID CYLINDER HAVING MOMENT OF INERTIA MR^2/2 (^2 MEANS SQUARE AND / DIVIDE)...SO IT MEANS MOMENT OF INERTIA OF P IS MORE THAN MOMENT OF INERTIA OF Q.!
AM I CORRECT?
 
joker94 said:
hi...can we consider P as a hollow cylinder then moment of inertia about the axis(which is passing through its centre) would be MR^2...AND THEN WE CAN CONSIDER Q AS A SOLID CYLINDER HAVING MOMENT OF INERTIA MR^2/2 (^2 MEANS SQUARE AND / DIVIDE)...SO IT MEANS MOMENT OF INERTIA OF P IS MORE THAN MOMENT OF INERTIA OF Q.!
AM I CORRECT?

Right answer, though of course it would be better not to have to assume the extreme case when the original question was posed more generally.
How about your questions 2 and 3?
 

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