Parallel And Perpendicular Axis Theorem Pdf File

Parallel and perpendicular axis theorem pdf file

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Rigid Body A rigid body is defined as a solid body in which the particles are compactly arranged so that the inter-particle distance is small and fixed, and their positions are not disturbed by any external forces applied on it. A rigid body can undergo both translational and rotational motion.

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A rigid body is said to have translator motion if it moves bodily from one plate to another. The motion of a car is the translator in nature. A rigid body is said to be in rotational motion about a fixed axis when its particles generate concentric circles with the same angular velocity but different linear velocities.

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The motion of a wheel of a train about its axle is rotational motion. The inertness or inability of a body to change its state of rest or uniform motion by itself is called inertia. In the case of linear motion, mass of the object determines the inertia of the body. As the mass of the body is high the inertia is also high and hence requires more force to move it to change the state of that body.

Parallel and perpendicular axis theorem pdf file

Similarly, in case of rotational motion if the moment of inertia is the high large amount of rotational force i. Similarly in rotational motion, a body rotating about an axis opposes any change desired to be produced in its state. This inertia is the rotational motion of the body is called rotational inertia. Consider a rigid body consisting a large number of small particles of mass m 1 , m 2 , m 3 , …..

As shown in the figure.

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Where, m i is the mass of the i th particle and r i is the perpendicular distance from the axis of rotation. Hence, In SI-units, the unit of moment of inertia is kg m 2. In CGS-system, its unit is g cm 2.

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The dimensional formula of the moment of inertia is [ML 2 T 0 ]. Where I cm is the moment of inertia about the parallel axis through the centre of mass, M is the total mass of the body and r is the distance between two axes. We have to calculate the moment of inertia of the rotating body of mass M about AB.

Parallel and perpendicular axis theorem pdf file

Suppose m be the mass of point object which is at a distance x from the centre of mass. Then, equation i can be written as. That is the moment of inertia of the body about the axis AB is the sum of its moment of inertia about the parallel axis CD through its centre of mass and the product of mass of the body and square of the distance between the two axes. This is the theorem of parallel axis.

Parallel Axis Theorem Formula

Let I x , I y and I z be the moments of inertia of plane lamina three mutually perpendicular axes passing through the point O. Let OX and OY be two mutually perpendicularly axes in the plane of the lamina and OZ be an axis passing through O and perpendicular to the plane of lamina. The moment of inertia of the inertia of the entire body about the OZ-axis is given by.

Parallel and perpendicular axis theorem pdf file

A rigid body is defined as a solid body in which the particles are compactly arranged so that the inter-particle distance is small and fixed, and their positions are not disturbed by any external forces applied on it.

The moment of inertia of the rigid body about a given axis of rotation is the sum of the product of the masses of the various particles and square of their perpendicular distances from the axis of rotation.

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What is Parallel Axis Theorem?

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Parallel and perpendicular axis theorem pdf file

Please Wait Cancel Report. Moment of Inertia The inertness or inability of a body to change its state of rest or uniform motion by itself is called inertia. Very Short Questions.

Parallel and perpendicular axis theorem pdf file

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Theorems of Parallel and Perpendicular Axis

Remember me. Login Cancel Register Forget Password? I want to know physically moment of inertia. Jan 19, Reply 0 Replies.

9. Parallel axis theorem & perpendicular axis theorem - theorem of moment of inertia - class 11