You probably dont care but if you are stoned like me during the covid times then you can watch all the new series on instaflixxer. I've been binge watching with my brother for the last months xD
Polar moment of inertia is an area moment of inertia. It measures the distribution of an area around an axis. The mass moment of inertia relates to the distribution of mass. They are related quite closely if the body is prismatic (has the same cross-section along the axis you are measuring the distribution) and has a uniform density. So polar moment of inertia would be the integral of r^2 * dA, while the mass moment of inertia would be the integral of r^2 * dm.
Good morning sir, since the Mass Moment of Inertia is more for bigger radius cylinder summation of translation K.E. and rotational K.E. should make bigger cylinder go to the bottom of the inclined plane first since M.I is more in bigger cylinder. But this is not happening. Could you explain sir?
@@DrRans Thank you, sir. Your learning materials on Mechanics of Materials are easy to understand and imparts knowledge. I request to come ahead with a course on Advanced Mechanics of Materials.
Explained the what is is pretty well but you haven't explained why it is at all . Why does the excess kinetic energy means (excess cuz its r2 so if you mass sits further you have more) more resistance? why does it make it harder to transition from potential Energy to kinetic ?
It’s not that there is excess kinetic energy, but that more kinetic energy is needed for the same movement. So in the experiment, both objects had the same potential energy, and that potential energy is converted to kinetic energy, but due to the distribution of mass in the hollow cylinder a lower velocity of the cylinder is obtained. So both cylinders have the same kinetic energy at the end, but the velocities are different due to the mass distribution. So equate the kinetic energies of two rolling cylinders with different mass distributions, and you will see that the linear velocity of the cylinder with a more mass away from the centroid will have a smaller linear velocity for the same amount of energy.
@@DrRans Thank you for your answer :) I see what you mean especially in a equation manner E= 1/2 (int(r^2)dm) .w^2 aka if you increase the r^2 you reduce w but velocity is w.r therefore velocity should be constant since mass is the same . Also forgetting about what we talked what is not intiutive about this concept ( I am not denying it or saying its wrong I am just trying to reaally understand it ). How exactly does at the t=0 moment the first rotation has more interia against the movement since ( again I know the formula and the basic linear logic from that but lets do it verbally) the partical at top sits very high and also since it sits high r is high , okey we say w is low but why exactly , what kind of nature forces cause this. Like it is the same mass there fore same total energy at t=0
@@rocketman99 At t = 0, both of the cylindars are at the same height, so they have the same potential energy (because their total mass is the same). Potential energy would be mass times height. Actually, there is a smal error here as the hollow sylindar has a higher centre of mass, so it actually has a little more potential energy than the solid cyinder, but even with this little extra energy, it has more resistance to rolling and thus rolls slower as a result of its resistance. To try an understand it verbally, it can be useful to think about the distance each bit of mass on the cylinder travels. In the hollow cylinder, in addition to the displacement in the direction of the ramp, mass is moving perpendicular as it is rolling. So the hollow cylinder, due to its larger radius, requires the mass to move perpendicular (lets call this up and down) relative to the ramp, and thus this added motion consumes some of the energy. So less energy is available for imparting velocity in the direction of the ramp.
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Excellently explained😇
Very good explanation
Thankyou for the elaborate explanation!
Nicely explained
I am planning to apply for masters in TU Delft. Hope to meet you soon :)
You probably dont care but if you are stoned like me during the covid times then you can watch all the new series on instaflixxer. I've been binge watching with my brother for the last months xD
@Lance Karsyn Definitely, I've been watching on instaflixxer for months myself =)
It is so helpful
Thank u so much sir
is the polar moment of inertia same as mass moment of inertia?
Polar moment of inertia is an area moment of inertia. It measures the distribution of an area around an axis. The mass moment of inertia relates to the distribution of mass. They are related quite closely if the body is prismatic (has the same cross-section along the axis you are measuring the distribution) and has a uniform density. So polar moment of inertia would be the integral of r^2 * dA, while the mass moment of inertia would be the integral of r^2 * dm.
Good morning sir, since the Mass Moment of Inertia is more for bigger radius cylinder summation of translation K.E. and rotational K.E. should make bigger cylinder go to the bottom of the inclined plane first since M.I is more in bigger cylinder. But this is not happening. Could you explain sir?
@@DrRans Thank you, sir. Your learning materials on Mechanics of Materials are easy to understand and imparts knowledge. I request to come ahead with a course on Advanced Mechanics of Materials.
Explained the what is is pretty well but you haven't explained why it is at all . Why does the excess kinetic energy means (excess cuz its r2 so if you mass sits further you have more) more resistance? why does it make it harder to transition from potential Energy to kinetic ?
It’s not that there is excess kinetic energy, but that more kinetic energy is needed for the same movement. So in the experiment, both objects had the same potential energy, and that potential energy is converted to kinetic energy, but due to the distribution of mass in the hollow cylinder a lower velocity of the cylinder is obtained. So both cylinders have the same kinetic energy at the end, but the velocities are different due to the mass distribution. So equate the kinetic energies of two rolling cylinders with different mass distributions, and you will see that the linear velocity of the cylinder with a more mass away from the centroid will have a smaller linear velocity for the same amount of energy.
@@DrRans Thank you for your answer :)
I see what you mean especially in a equation manner E= 1/2 (int(r^2)dm) .w^2 aka if you increase the r^2 you reduce w but velocity is w.r therefore velocity should be constant since mass is the same . Also forgetting about what we talked what is not intiutive about this concept ( I am not denying it or saying its wrong I am just trying to reaally understand it ). How exactly does at the t=0 moment the first rotation has more interia against the movement since ( again I know the formula and the basic linear logic from that but lets do it verbally) the partical at top sits very high and also since it sits high r is high , okey we say w is low but why exactly , what kind of nature forces cause this. Like it is the same mass there fore same total energy at t=0
@@rocketman99 At t = 0, both of the cylindars are at the same height, so they have the same potential energy (because their total mass is the same). Potential energy would be mass times height. Actually, there is a smal error here as the hollow sylindar has a higher centre of mass, so it actually has a little more potential energy than the solid cyinder, but even with this little extra energy, it has more resistance to rolling and thus rolls slower as a result of its resistance.
To try an understand it verbally, it can be useful to think about the distance each bit of mass on the cylinder travels. In the hollow cylinder, in addition to the displacement in the direction of the ramp, mass is moving perpendicular as it is rolling. So the hollow cylinder, due to its larger radius, requires the mass to move perpendicular (lets call this up and down) relative to the ramp, and thus this added motion consumes some of the energy. So less energy is available for imparting velocity in the direction of the ramp.
@@DrRans thank you soo much that was really helpfull
UwU