Question

Relation between the contour length and radius of gyration

Answer 1

Answer:

Radius of gyration or gyradius of a body about an axis of rotation is defined as the radial distance of a point, from the axis of rotation at which, if whole mass of the body is assumed to be concentrated, its moment of inertia about the given axis would be the same as with its actual distribution of mass. It is denoted by Gs

Mathematically the radius of gyration is the root mean square distance of the object's parts from either its center of mass or a given axis, depending on the relevant application. It is actually the perpendicular distance from point mass to the axis of rotation.

Suppose a body consists of {\displaystyle n} n particles each of mass {\displaystyle m} m. Let {\displaystyle r_{1},r_{2},r_{3},\dots ,r_{n}} {\displaystyle r_{1},r_{2},r_{3},\dots ,r_{n}} be their perpendicular distances from the axis of rotation. Then, the moment of inertia {\displaystyle I} I of the body about the axis of rotation is

{\displaystyle I=m_{1}r_{1}^{2}+m_{2}r_{2}^{2}+\cdots +m_{n}r_{n}^{2}} {\displaystyle I=m_{1}r_{1}^{2}+m_{2}r_{2}^{2}+\cdots +m_{n}r_{n}^{2}}

Answer 2

Answer:

Radius of gyration or gyradius of a body about an axis of rotation is defined as the radial distance of a point, from the axis of rotation at which, if whole mass of the body is assumed to be concentrated, its moment of inertia about the given axis would be the same as with its actual distribution of mass. It is denoted by Gs

Mathematically the radius of gyration is the root mean square distance of the object's parts from either its center of mass or a given axis, depending on the relevant application. It is actually the perpendicular distance from point mass to the axis of rotation.

Suppose a body consists of {\displaystyle n} n particles each of mass {\displaystyle m} m. Let {\displaystyle r_{1},r_{2},r_{3},\dots ,r_{n}} {\displaystyle r_{1},r_{2},r_{3},\dots ,r_{n}} be their perpendicular distances from the axis of rotation. Then, the moment of inertia {\displaystyle I} I of the body about the axis of rotation is