The radius of gyration of any body about the axis of rotation could be defined as the radial distance to a point which would have a moment of inertia the same as the body’s actual distribution of mass if the total mass of the body were concentrated there. It is denoted by k, and the radius of gyration is given as,
mm is the unit of the radius of gyration.
In mathematical form, the radius of gyration is the root mean square distance of the object’s parts from either its centre of mass or a given axis, depending on the relevant application. Or, it is actually the perpendicular distance from point mass to the axis of rotation. One can represent the trajectory of a moving point as a body. Then, the radius of gyration can be used to characterise the typical distance travelled by this point.
The radius of gyration can also be defined as the root mean square distance of the body’s various particles from the axis of rotation. In other words, the radius of gyration is a measure of how the mass of a rotating rigid body is distributed around its axis of rotation.
We can represent this in mathematical form as,
Read More – Radius of Gyration
Important Questions with Answers
1. Give the significance of “radius of gyration.”
The significance of radius of gyration:
- The radius of gyration plays an important role in determining the pressure exerted at a particular point.
- We can estimate the intensity and the strength between the given cross-section of an area by using the radius of gyration.
- If the mass of the particle is distributed away from the axis of rotation, then the radius of gyration will be more.
2. On what factors does the radius of gyration depend?
The radius of gyration does not depend on the mass of an object, but it depends on the size and the shape of the object. It also depends on the position and arrangement of the rotational axis. Likewise, it also depends upon mass distribution with respect to the rotational axis of the object.
3. What is the radius of the gyration of an object in rotational motion?
The radius of gyration of an object about an axis of rotation is defined as the radial distance to a point from the rotational axis, which would have a moment of inertia the same as an object’s actual distribution of mass if the total mass of the object were concentrated there.
4. What is the centre of gyration?
When studying the axis of a spinning body, the centre of gyration can be viewed as a point at which the body’s moment of inertia would remain unaltered if the entire mass of the body were concentrated. The radius of gyration can be defined as the distance between this point and the axis.
6. The radius of gyration is a constant quantity.
A. True
B. False
Answer – B. False
The radius of gyration is not a constant quantity. The radius of gyration depends on the axis of rotation and distribution of mass.
7. What is the use of the radius of gyration?
The radius of gyration is used to examine how different structural shapes will behave when compressed along one axis. It is employed in the prediction of buckling in a compression beam or member.
8. Which factors affect the gyration radius?
Two factors influence the estimation of the radius of gyration: size and state of a body. In other words, it is the positioning and arrangement of the rotational axis. Additionally, mass appropriation is required in relation to the rotational axis of the body.
9. What is the purpose of calculating the radius of gyration?
A radius of gyration is used to compare the behaviour of different structural shapes under compression along an axis. Predicting buckling in compression beams or members is achieved using this method.
10. Describe how the gyroradius is used.
For segments with plane areas and cross-sectional areas, the radius of gyration is used as an integral for calculating the clasp’s position around the pivot. Usually, this is done in engineering since the bodies are continuous chunks of matter that need to be integrally calculated.
In molecular physics, the radius of gyration is used to determine the dimensions of the polymer chain. It has been demonstrated that the radius of gyration is proportional to the root mean square distance between the given monomers. When it comes to molecular physics, the radius of gyration is measured as an average over time.
Practice Questions
- Is the radius of gyration scalar or vector?
- Why is the radius of gyration squared?
- What is the radius of gyration of a solid sphere about its diameter?
- What is the formula of gyration?
- What is the SI unit of moment of inertia?
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