A2
Moment of inertia is the term used to measure or quantify the amount of mass located at an object's extremities. For example if all the mass of an object was located in a small compact size (like a lead ball) its moment of inertia would be small compared to the same amount of mass shaped into a dumbell. Because a dumbell has most of its mass located farther from its center. But there is a "qualification" here. Moment of inertia is calculated relative to a hypothetical spin axis. Once you choose the spin axis then you calculate the moment of inertia by multiplying the mass times its distance to the spin axis squared; I = MR^2
So in the example between the sphere and the dumbell the moment of inertia of the dumbell would be significantly larger relative to a spin axis perpendicular to the dumbell length. If you instead choose your spin axis to lie thru the dumbell parallel to its length then its moment of inertia,relative to this axis, would be much smaller because the mass would be located closer to that axis. And ,in fact, it might even be smaller then the moment of inertia of a sphere about an axis thru its center.
A way to store kinetic energy is with a spinning object. In calculating how much energy would be stored in a spinning object the energy is proportional to the moment of inertia. So all other things being equal you would choose a spin axis and object shape that gave you the largest moment of inertia for maximum stored energy.
SIMPLY "MOI" MEANS
Moment of inertia is the characteristic of an object to resist rotation.
T IS DIRECTLY PROPORTIONAL TO I
where
T is the torque applied to the object
I is the moment of inertia of the object
I Depends on following elements
mass of the element .
Distance of the element from the axis of rotation.
For finding I (Application purpose) for Different sections we must know how to find out Center of gravity of a Section.
The moment of inertia of a molecule is the mass property that is held by a molecule. This determines the necessary torque of a desired angular acceleration concerning the axis of rotation.
Polar moment of inertia of an area is a quantity used to predict an object's ability to resist torsion.Moment of inertia, also called mass moment of inertia or the angular mass, (SI units kg m2, Imperial Unit slug ft2) is a measure of an object's resistance to changes in its rotation rate.
How do to determine the moment of inertia of a cub
Moment of Inertia of a disk (I) = 1/2MR2 Moment of Inertia of a disk (I) = 1/4MR2
mass moment of inertia is the property of the body to resist rotation about the given axis where as the area moment of inertia is the resistance to bending about the given axis
moment of inertia is basically an objects resistance to its state of motion.
Moment of inertia has unit kg m2
The unit of Inertia is kg and the Moment of Inertia is kg*m^2
Polar moment of inertia of an area is a quantity used to predict an object's ability to resist torsion.Moment of inertia, also called mass moment of inertia or the angular mass, (SI units kg m2, Imperial Unit slug ft2) is a measure of an object's resistance to changes in its rotation rate.
Comparing linear and circular motion we can see that moment of inertia represents mass and torque represents force. So the product change in the circular momentum per unit time is torque. Circular momentum is the product of moment of inertia and circular velocity.
How do to determine the moment of inertia of a cub
Moment of Inertia of a disk (I) = 1/2MR2 Moment of Inertia of a disk (I) = 1/4MR2
Dimensional formula of moment of inertia = [ML2T0 ]
The second moment of a force is called as moment of inertia.
mass moment of inertia is the property of the body to resist rotation about the given axis where as the area moment of inertia is the resistance to bending about the given axis
Since inertia is represented numerically by an object's mass. Unit of inertia in S.I UNIT is Kilogram
define moment of inertia§ I is the moment of inertia of the mass about the center of rotation. The moment of inertia is the measure of resistance to torque applied on a spinning object (i.e. the higher the moment of inertia, the slower it will spin after being applied a given force).
moment of inertia is basically an objects resistance to its state of motion.