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Zubair Ahmad
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For radius of gyration we say distance from axis to a point where would mass is concentrated. isn't that center of mass?
No, that is not the correct definition of radius of gyration. The radius of gyration, r, is the perpendicular distance to the axis of rotation of a point mass whose moment of inertia (I=mr^2) is the same moment of inertia of the actual object having that same mass. So say an object having 10 kg of mass with an I of 1000 kg-m^2 is equivalent to a point mass of 10 Kg located10 meters away from the axis, so r = 10 m. In other words, r = sq rt (I/m).Zubair Ahmad said:For radius of gyration we say distance from axis to a point where would mass is concentrated. isn't that center of mass?
No, we have a single point where IF the whole mass was concentrated there, the moment of inertia would be equivalent to the moment of inertia of the object. A symmetrical object for example has its actual center of mass at the center of it at the rotation axis, but its radius of gyration is not 0, it is sq rt (I/m)Zubair Ahmad said:But physically we have a single point where we say whole mass is concentrated.
No, sir. The center of mass is real; the radius of gyration is imaginaryZubair Ahmad said:So can we say physically there are two such points
The radius of gyration is a measure of the distribution of mass around an axis. It represents the distance from the axis at which the entire mass of an object could be concentrated to produce the same moment of inertia as the actual distribution of mass.
The radius of gyration can be calculated by taking the square root of the ratio of the moment of inertia of the object to its mass. It can also be calculated by dividing the length of the object by 2 for a point mass or by using the parallel axis theorem for a distributed mass.
The radius of gyration and mass concentration have an inverse relationship. As the mass concentration increases, the radius of gyration decreases. This means that a more concentrated mass distribution has a smaller radius of gyration, while a more spread out mass distribution has a larger radius of gyration.
The radius of gyration is an important factor in structural engineering as it helps determine the stability and strength of a structure. A smaller radius of gyration indicates a more compact and stable structure, while a larger radius of gyration can lead to instability and failure.
The radius of gyration is a key factor in the performance of rotating objects such as a spinning top or a rotating wheel. A smaller radius of gyration allows for faster rotation and smoother movement, while a larger radius of gyration can cause wobbling and instability.