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the moment of inertia of a body about a given axis is equal to the sum of its moment of inertia about a parallel axis passing through its centre of mass and the product of its mass and square of perpendicular distance between two axis

Iz=Ix+Iy

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Q: State and prove the parallel axis theorem?
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State and prove perpendicular axis and parallel axis theorem?

In physics, the perpendicular axis theorem (or plane figure theorem) can be used to determine the moment of inertia of a rigid object that lies entirely within a plane, about an axis perpendicular to the plane, given the moments of inertia of the object about two perpendicular axes lying within the plane. The axes must all pass through a single point in the plane.Define perpendicular axes , , and (which meet at origin ) so that the body lies in the plane, and the axis is perpendicular to the plane of the body. Let Ix, Iy and Iz be moments of inertia about axis x, y, z respectively, the perpendicular axis theorem states that[1]This rule can be applied with the parallel axis theorem and the stretch rule to find moments of inertia for a variety of shapes.If a planar object (or prism, by the stretch rule) has rotational symmetry such that and are equal, then the perpendicular axes theorem provides the useful relationship:


State ane prove perpendicular axis theorem?

The perpendicular axis theorem states that the moment of inertia of a planar object about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two perpendicular axes lying in the plane of the object and intersecting the first axis. This theorem can be proven using the parallel axis theorem and considering the individual moments of inertia about each axis. The perpendicular axis theorem is commonly used to find the moment of inertia of thin planar objects.


If moment of inertia of a body change of axis of rotation?

If the moment of inertia of a body changes due to a change of axis of rotation, the new moment of inertia can be calculated using the parallel axis theorem. This theorem states that the moment of inertia about a new axis parallel to the original axis can be found by adding the mass of the body multiplied by the square of the distance between the two axes.


Moment of inertia of parallel axis?

This is known as parallel axes theorem. Statement: If IG be the moment of inertia of a body of mass M about an axis passing through its centre of gravity, then MI (I) of the same body about a parallel axis at a distance 'a' from the previous axis will be given as I = IG + M a2


What is the moment of inertia of a rod?

The moment of inertia of a cube depends on what its axis of rotation is. About an axis perpendicular to one of its sides and through the centre of the cube is (ML2)/6. Where M is the Mass of the Cube and L the length of its side. Due to the symmetry of the cube, you can find the Moment of Inertia about almost any other axis by using Parallel and Perpendicular Axis Theorems.


The line y equals -2.5 is parallel to what axis?

y=-2.5 is parallel to the x axis. The equation of the x axis is y=0


State Perpendicular axis theorem?

if xx and yy be the two axes and the moment of inertia of them be Ixx and Iyy then the moment of inertia about the zz axes will be Izz


What line is parallel to the y-axis?

Any line with the equation [ x = any number ] is parallel to the y-axis.


What is the slope of a line that is parrel to the y- axis?

The slope (or gradient) if the line is parallel to the y-axis, is infinite. If it's parallel to the x-axis the slope is zero.


What is a straight line parallel to an axis called?

It's called an ORDINATE. when there is a straight line 100% parallel to the x axis, it's slope is 0. If a line is parallel to the y axis, its slope is undefined, or infinite.


Which equation represents a line parallel to the x axis?

[ y = plus or minus any number ] is parallel to the x-axis.


What can you conclude about the state of motion of an object if displacement time graph is parallel to the time axis?

If the displacement-time graph is parallel to the time axis, the object is at rest. This is because the displacement is not changing over time, indicating that the object is not moving.