Why radius of gyration is zero when body slides
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When body slides of the gyration is zero
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The moment of inertia (I)(I) of an object is a mass property which is commonly used to determine angular acceleration about a rotational axis for a given applied torque.
Consider a solid disk with radius = RR and total mass = mm.
The moment of inertia of a disk about the rotational axis passing through the center is Ix=12mR2Ix=12mR2
Since it is a solid disk, the mass of the disk is uniformly distributed across the area of the disk. Now imagine that we somehow take the total mass and concentrate it at a radius = kk as shown above right, so that the resulting thin-walled disk has the same moment of inertia as the solid disk. The radius at which they have the same inertia is called the “radius of gyration” and is usually denoted by the letter “kk”
k=Im−−√k=Im
If an object has mass, then it will have mass moment of inertia. And the magnitude of the inertia will depend on the chosen axis of rotation. Therefore, if an object has inertia, you can calculate the radius of gyration using the above formula.
Consider a solid disk with radius = RR and total mass = mm.
The moment of inertia of a disk about the rotational axis passing through the center is Ix=12mR2Ix=12mR2
Since it is a solid disk, the mass of the disk is uniformly distributed across the area of the disk. Now imagine that we somehow take the total mass and concentrate it at a radius = kk as shown above right, so that the resulting thin-walled disk has the same moment of inertia as the solid disk. The radius at which they have the same inertia is called the “radius of gyration” and is usually denoted by the letter “kk”
k=Im−−√k=Im
If an object has mass, then it will have mass moment of inertia. And the magnitude of the inertia will depend on the chosen axis of rotation. Therefore, if an object has inertia, you can calculate the radius of gyration using the above formula.
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Acc to my book K2/R2 =0 when body slides ?so why is it
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