Moment of inertia of two cylinders placed vertically

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SUMMARY

The discussion centers on the moment of inertia of two vertically stacked cylinders, with a motor in the top cylinder intended to rotate the bottom cylinder. Participants clarify that the moment of inertia should account for the entire system's mass, including both cylinders. The conversation highlights that without a fixed frame, the top cylinder will rotate in the opposite direction to the bottom cylinder when the motor is activated. To effectively drill into wood, the setup must be stabilized, as the lack of a fixed frame will prevent the bottom cylinder from rotating independently.

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  • Understanding of moment of inertia and angular momentum
  • Basic knowledge of Newton's laws of motion
  • Familiarity with mechanical systems involving motors and levers
  • Concept of torque and its application in rotational systems
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ahmed11
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if i have two cylinders with same mass and radius placed over each other vertically and there is a motor inside the top cylinder welded in the cylinder itself, and connected to the bottom cylinder to rotate the bottom cylinder. assume it's the whole thing is resting on the ground and neglect friction with ground. if i try to calculate the moment of inertia of the bottom cylinder for the motor to rotate should i put the mass of the bottom cone only or add the mass of the whole thing? and if yes add all the mass, how to manipulate the whole thing to make the motor rotate the bottom cylinder instead of the top one. what i have in mind is if the mass of top cylinder with motor is 10 kg and bottom is 5kg i just have to change the length of lever which is between motor and top cylinder and make it shorter than the lever in the bottom cylinder between the shaft of motor inside the bottom cylinder welded to the walls of bottom cylinder so actually changing the radius of the bottom cylinder. Hope this makes sense
 
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the whole object is just hanged by a cable (no fixed frame)
 
By Newton's third law, rotating the bottom one also rotate the top one.
 
Khashishi said:
By Newton's third law, rotating the bottom one also rotate the top one.
could you please elaborate more, will both cylinders rotate or only top or bottom?
i'm really confused about this and also regarding the moment of inertia of the whole thing or is it separate
 
Angular momentum is conserved. So if you use a motor to turn one half, the other half will turn in the other direction.

Can you draw your setup? I don't understand what you mean by some things.
 
here is a rough drawing of what i mean.
if my motor rotates both sides as you said, now how to make the bottom rotate and drill in wood vertically without any fixed frame just like drawing only weight of the whole thing. will it drill in wood and rotate top bottom or because there is no fixed frame it will rotate only top cylinder with motor in opposite direction; if so then is there a way that i can manipulate the length of the lever from motor to cylinder and the lever from motor shaft to cylinder wall (bottom cylinder, the one that will drill in wood and assume it has teeth)
 

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If you don't want the top to rotate, you have to attach it to something.
 
Khashishi said:
If you don't want the top to rotate, you have to attach it to something.
My main concern is the bottom to rotate and drill in wood
But what I think will happen because there is no fixed frame the motor in top will rotate relatively and bottom will stay stationary due the contact with wood
 
Yup. That's exactly what will happen. It sounds like you have a power drill dangling from a wire. You can't hope to drill wood unless you hold the drill with your hands or mount it to something.
 
  • #10
Another option is to use two drills rotating in opposite directions to cancel out the rotation.
 
  • #11
Khashishi said:
Another option is to use two drills rotating in opposite directions to cancel out the rotation.
what do you mean by two drills in opposite direction cancel out the rotation.
would you please explain in details and if possible attach a video so i can see how to do it.
i would really appreciate it
thank you
 
  • #12
What comes to mind is a sort of Forstner bit with a hole in the center through which a counter-rotating regular bit would fit. The hope would be that the torques from the two bits would be equal and opposite. Quite impractical though. It is far easier to just hold onto the drill.
 
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