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What is the physical significance of moment of inertia is radius of gyration a constant quantity?
For any body rotating about a given axis, it is possible to find a radial distance from the axis where, if the whole mass of the body is supposed to be concentrated, its moment of inertia remain unchanged. This radial distance is called radius of gyration.
What is radius of gyration write formula?
Radius of Gyration Formula The formula of moment inertia in terms of the radius of gyration is given as follows: I = mk2 (1) where I is the moment of inertia and m is the mass of the body. Accordingly, the radius of gyration is given as follows. k=√Im k = I m (2)
What is physical meaning of moment of inertia?
moment of inertia, in physics, quantitative measure of the rotational inertia of a body—i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of a torque (turning force).
What is the physical significance of MI?
Answer: The physical significance of the moment of inertia is similar to the mass in the translational motion. In translational motion, the mass of a body is used for measuring the inertia. As the mass increases, inertia becomes larger. The force required for producing the linear acceleration will also increase.
What is radius of gyration in civil engineering?
Radius of gyration is used to describe the distribution of cross sectional area in a column around its centroidal axis. Sponsored Links. In structural engineering the Radius of Gyration is used to describe the distribution of cross sectional area in a column around its centroidal axis.
What is the unit of radius in physics?
“Radius is a straight line from the center to the boundary (Also known as ‘Circumference’ or ‘Perimeter’) of a circle or sphere”. The above definition makes it clear that radius is a kind of length and as we know, the SI unit of length is meter (m).
Why is it useful to define radius of gyration Class 12?
Physical significance: The radius of gyration is less if I is less, i.e., if the mass is distributed close to the axis; and it is more if I is more, i.e., if the mass is distributed away from the axis. Thus, it gives an idea about the distribution of mass about the axis of rotation.
What is the physical meaning of moment?
In physics, a moment is an expression involving the product of a distance and physical quantity, and in this way it accounts for how the physical quantity is located or arranged. In principle, any physical quantity can be multiplied by a distance to produce a moment.
What is the definition of radius of gyration in physics?
It is actually the perpendicular distance from point mass to the axis of rotation. One can represent a trajectory of a moving point as a body. Then radius of gyration can be used to characterize the typical distance travelled by this point. . Let be their perpendicular distances from the axis of rotation. Then, the moment of inertia .
What is the radius of gyration for polymer chains?
A radius of gyration in general is the distance from the center of mass of a body at which the whole mass could be concentrated without changing its moment of rotational inertia about an axis through the center of mass. For a polymer chain, this is also the root-mean-square distance of the segments of the molecule from its center of mass.
What is the formula for moment of inertia and radius of gyration?
The formula of moment inertia in terms of the radius of gyration is given as follows: I = mk 2 (1) where I is the moment of inertia and m is the mass of the body. Accordingly, the radius of gyration is given as follows. \\(k=\\sqrt{\\frac{I}{m}}\\) (2) The unit of radius of gyration is mm.
What happens if the principal moment of gyration is not equal?
If the principal moments of the two-dimensional gyration tensor are not equal, the column will tend to buckle around the axis with the smaller principal moment. For example, a column with an elliptical cross-section will tend to buckle in the direction of the smaller semiaxis.