RADIUS OF GYRATION:
- Radius of Gyration is the distance from the axis of rotation to a point where all of the mass or area can be concentrated to yield the same resistance to angular motion.
- An averaging out of the radii (r) of all the mass particles. This allows all the mass or area to be represented by a single radius (k).
- 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.
I = mk² or I = Ak²
- The distribution of an object’s mass has a much The distribution of an object’s mass or area has a much greater affect on the moment of inertia than mass.
Principal Axes for any Object
Maximum Moment of Inertia Axis (Imax): It is the Axis along which the moment of inertia is largest i.e. maximum moment of inertia.
Minimum Moment of Inertia Axis (Imin): It is the Axis along which the moment of inertia is smallest i.e. minimum moment of inertia.
Intermediate Moment of Inertia Axis (Iint): It has an intermediate moment of inertia. Determined not by its moment of inertia value, but rather because it is perpendicular to the both Imax and Imin. Note: All three axes are perpendicular to each other
Note: All three axes are perpendicular to each other.
Use of Radius of Gyration
Calculating the radius of gyration is relatively easy, so it is often used to study various dynamic systems. For example,
- In the molecular system, we can use the radius of gyration (K) to measure the effective size of a polymer. If the value of K is small, then we can say the polymer is relatively compact.
- Similarly, in structural engineering, we can use K to measure the stiffness of the column.
- We can also use the radius of gyration to determine the distribution of the mass in the axis of rotation. If the value of K is small, then the mass is close to the axis of rotation. However, if K is large, the mass is far from the axis of rotation.
RELATED VIDEOS FOR RADIUS OF GYRATION: