.00288 kgm^2
The moment of inertia of a hollow cylinder can be calculated with the help of the formula, I=0.5xMxRxR. Here I is inertia, M is mass and R is the radius.
Mass and radius
Ans : By the formula of moment of inertia , I=mr2 (2=square) As by the formula it is clear that the moment of inertia depends on the mass and the radius of a particular body , so as the mass increases moment of inertia will considerably increase , So as the water drips into the beaker the mass of the beaker will increase By the law of conservation of angular momentum Moment of inertia is inversely proportional to the angular velocity ( omega ) , Since in the above case of coasting rotating system moment of inertia is increased so the angular velocity (omega) will also decrease and hence the coasting rotating system will now rotate slowly as compared to its rotation before dripping water !
mass, velocity and radius
The answer will depend on whether the axis isthrough the centre of the disk and perpendicular to its plane,a diameter of the disk, orsome other axis.Unless that information is provided, the answer is meaningless.
The moment of inertia of a hollow cylinder can be calculated with the help of the formula, I=0.5xMxRxR. Here I is inertia, M is mass and R is the radius.
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.
mass moment of inertia for a solid sphere: I = (2 /5) * mass * radius2 (mass in kg, radius in metres)
(1/2)mr^2 where m=mass r=radius
I believe it is I = mk^2 where k is radius of gyration and m is mass.
It is the square root of ratio moment of inertia of the given axis to its mass.
Its diameter is 2R, whatever the mass.
It can be done, but it would require taking an integral for the moment of inertia of each particle of the disc... something i don't have the time to do right now ^^;
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
radius of gyration = sqrt(Moment of inertia/cross section area) Regards, Sumit
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.
Basically radius of gyration of a substance is defined as that distance from the axis of rotation from which if equivalent mass that of the substance is kept will have exactly the same moment of inertia about that axis of the substance.