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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
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∙ 14y ago
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The moment of inertia of a solid cylinder is?
the moment of inertia of a solid cylinder about an axis passing through its COM and parallel to its length is mr2/2 where r is the radius.
What increase the moment of inertia?
A rotating body that spins about an external or internal axis (either fixed or unfixed) increase the moment of inertia.
What is the Moment of Inertia of a Rectangle about the axis passed through its diagonal?
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What is the moment of inertia of a cylinder?
(1/2) mr2, assuming the axis of rotation goes through the center, and along the axis of symmetry.
What is meant by Radius of gyration?
It is the square root of ratio moment of inertia of the given axis to its mass.
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.
State and prove the parallel axis theorem?
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
The moment of inertia of a solid cylinder is?
the moment of inertia of a solid cylinder about an axis passing through its COM and parallel to its length is mr2/2 where r is the radius.
Define radius of gyration state s.i. units of moment of inertia and give its dimensions?
The Radius of Gyration of an Area about a given axis is a distance k from the axis. At this distance k an equivalent area is thought of as a line Area parallel to the original axis. The moment of inertia of this Line Area about the original axis is unchanged.
What is moment of inertia of partially filled tube with liquid and set horizontal rotating about a vertical axis passing through its center?
The moment of inertia of a partially filled tube with liquid rotating horizontally about a vertical axis through its center is affected by the distribution of mass within the tube. The moment of inertia depends on the shape of the tube, the mass of the liquid, the radius of the tube, and the distance of the liquid's center of mass from the rotation axis. The parallel axis theorem can be used to calculate the moment of inertia of the tube and liquid system.
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.
What is the moment of inertia about an axis of rotation body?
The moment of inertia of a body about an axis of rotation is a measure of its resistance to rotational motion. It depends on the mass of the body and how that mass is distributed around the axis of rotation. A body with a larger moment of inertia requires more torque to rotate at the same rate as a body with a smaller moment of inertia.
Moment of inertia for triangular section?
The formula for the moment of inertia of a triangular section about its base is (1/36) * base * height^3. This formula assumes the triangular section has its base parallel to the axis of rotation.
What is the value of moment of inertia of ellipse about its centroidal axis?
If an ellipse has a radius A long the x-axis and B along the y-axis (A > B) then the moment of inertia about the x-axis is 0.25*pi*ab^3
Why is it necessary to mention the axis of rectangular bar while calculating the moment of inertia?
Mentioning the axis of a rectangular bar is necessary when calculating the moment of inertia because the moment of inertia depends on the axis chosen. The distance of the axis from the centroid affects the distribution of mass around that axis, which in turn affects the resistance to rotation. Different axes of rotation will yield different moment of inertia values for the same object.
A 4.2kg mass is placed at 3.04.0m Where can an 8.4kg mass be placed so that the moment of inertia about the z-axis is zero?
The moment of inertia about the z-axis is given by the equation I = mr^2, where m is the mass and r is the distance from the z-axis. For the moment of inertia to be zero, the mass must be placed at the origin (r=0) along the z-axis. So, the 8.4kg mass must be placed at the origin (0,0,0) to have a moment of inertia of zero about the z-axis.
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.
