Instantaneous moment of inertia of a circle
![instantaneous moment of inertia of a circle instantaneous moment of inertia of a circle](https://images.slideplayer.com/24/7502919/slides/slide_2.jpg)
There are three types of theorems that are very important with respect to Moment of Inertia:
![instantaneous moment of inertia of a circle instantaneous moment of inertia of a circle](https://i.ytimg.com/vi/idKWlkgKXzM/hqdefault.jpg)
Thus, the radius of gyration of a body about an axis is equal to the square root of the ratio of the body about that axis. Thus, the radius of gyration of a body is that perpendicular to the axis of rotation whose square multiplied by the mass of that body gives the moment of inertia of that body about that axis. If the mass and radius of gyration of the body is M and K respectively, then the moment of inertia of a body is The radius of gyration of a body is the perpendicular to distance from the axis of rotation to the point at which the moment of inertia obtained by taking the total mass of the body as the center is equal to the actual moment of inertia of the object. Note: After the change in the size or shape or axis of the body, the moment of inertia will be changed. It is clear from the equation that the moment of inertia of a body about an axis of rotation is equal to the sum of the product of the mass of each particle of that body and the square of its perpendicular distance from the axis of rotation.
![instantaneous moment of inertia of a circle instantaneous moment of inertia of a circle](https://img.einnews.com/ampsize/248877/one-sheet.jpeg)
Here I represent the moment of inertia of the whole body about the axis of rotation and the sign Σ represents the sum. Suppose a particle of mass m is moving with respect to the rotational axis XY, then the moment of inertia of the particle about XY will be I = mr 2Įxpression for Moment of Inertia of a body Mathematically, the product of the square of the mass of a particle and the distance from the axis of rotation is called the moment of inertia of the particle about the axis of rotation. The moment of inertia is a scalar quantity. Therefore, a body in rotational motion opposes the external force-moment applied to change its rotational state, this tendency is called its Moment of Inertia. this tendency of the body is called its Moment of Inertia. Similarly, everybody in rotational motion, whether it is moving about the axis of rotation or capable of rotating, but at rest, opposes the change caused by the external force. This tendency of an object is called its Inertia. According to Newton’s first law of motion, an object that is stationary will remain stationary and an object that is in motion will continue to move in a straight line with the same velocity unless an external force is applied to it, that is, an object can’t automatically change its position, but when an external force is applied on the object to change its position, then that object opposes it. Just as linear motion has inertia, so rotational motion has Moment of Inertia. “ When by applying a force or a couple of forces on a rigid body, that body stars rotating about an axis passing rotating about an axis passing through itself, then its motion is called Rotational Motion“. this motion of the body is called rotational motion and the axis about which the body rotates is called the rotational axis.
#Instantaneous moment of inertia of a circle free
If a body rests at a point in such a way that it is free to move around this point, then when an external force is applied to the body, it does not move in the direction of the force but moves along the axis passing through that point starts moving around.
![instantaneous moment of inertia of a circle instantaneous moment of inertia of a circle](http://www.mock4exam.org/wp-content/uploads/2017/05/20.png)
ISRO CS Original Papers and Official Keys.GATE CS Original Papers and Official Keys.