show that M.I play same roll in rotational motion as mass play in linear motion
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If you derive the equations for rotational motion of a rigid body about a fixed axis ,you find that these equations are similar to the equations of linear motion.
The linear displacement d is replaced by angular displacement ,(theta).
The linear velocity v is replaced by angular velocity w. Also, v=wX r.
Linear acceleration a=wXv+(alpha)X r ,where alpha is angular acceleration.
Force=ma is replaced by torque = rX F =I (alpha). Here, I is moment of inertia about the axis of rotation.
Angular momentum is Iw which similar to linear momentum, p=mv.
Kinetic energy of rotational motion is (1/2)Iw^2. This is similar to (1/2)mv^2.
The equation, torque=I ( alpha) corresponds to F=ma.
This last equation shows that moment of inertia I is inertia to the rotational motion as mass is inertia to the linear motion.
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Harold Kingsberg, Reader
Answered Mar 9, 2013
Okay, so let's perform a quick experiment. Keep your arms in close to your body and spin around as fast as you can, then stop suddenly. Do that again, this time with your arms out.
What you'll notice is that the second time, the top half of your body will twist a little more when you stop than it did the first time. The inertia of the upper half of your body is greater the second time than it is the first - it's that much harder to stop spinning. We can rule this out as having occurred because of an appreciable change in mass. So when it comes to rotation, inertia isn't only dependent upon mass, it's also dependent upon the position of that mass.
Another example: let's say you have a point mass (a geometric point that has some mass, which actually is pretty much the definition of a black hole, but is also a highly useful concept in modeling Newtonian physics) revolving around some central point at a radius R. Now let's say you have another point mass revolving around that same central point at a radius of 2R. If they both revolve around that central point at a rate of one revolution per minute, it's clear that the point mass at 2R is covering twice as much distance as the point mass at R. If the point masses have the same mass, then 2R has twice the momentum as R and four times the kinetic energy. The inertia of the 2R point mass is greater than that of the R point mas
The linear displacement d is replaced by angular displacement ,(theta).
The linear velocity v is replaced by angular velocity w. Also, v=wX r.
Linear acceleration a=wXv+(alpha)X r ,where alpha is angular acceleration.
Force=ma is replaced by torque = rX F =I (alpha). Here, I is moment of inertia about the axis of rotation.
Angular momentum is Iw which similar to linear momentum, p=mv.
Kinetic energy of rotational motion is (1/2)Iw^2. This is similar to (1/2)mv^2.
The equation, torque=I ( alpha) corresponds to F=ma.
This last equation shows that moment of inertia I is inertia to the rotational motion as mass is inertia to the linear motion.
374 Views · Answer requested by KUNDAN SINGH
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Promoted by Blinkist
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Harold Kingsberg, Reader
Answered Mar 9, 2013
Okay, so let's perform a quick experiment. Keep your arms in close to your body and spin around as fast as you can, then stop suddenly. Do that again, this time with your arms out.
What you'll notice is that the second time, the top half of your body will twist a little more when you stop than it did the first time. The inertia of the upper half of your body is greater the second time than it is the first - it's that much harder to stop spinning. We can rule this out as having occurred because of an appreciable change in mass. So when it comes to rotation, inertia isn't only dependent upon mass, it's also dependent upon the position of that mass.
Another example: let's say you have a point mass (a geometric point that has some mass, which actually is pretty much the definition of a black hole, but is also a highly useful concept in modeling Newtonian physics) revolving around some central point at a radius R. Now let's say you have another point mass revolving around that same central point at a radius of 2R. If they both revolve around that central point at a rate of one revolution per minute, it's clear that the point mass at 2R is covering twice as much distance as the point mass at R. If the point masses have the same mass, then 2R has twice the momentum as R and four times the kinetic energy. The inertia of the 2R point mass is greater than that of the R point mas
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