State the expression for moment of inertial of the following (1) A rod (2) rectangula plate (3) ring (4)circular disc
Nuts to the question. Moment of inertia depends not only on the size and shape of the object, it depends on the axis and placement of the axis of rotation. Goodness.
http://en.wikipedia.org/wiki/List_of_moments_of_inertia
Sure! The expressions for moment of inertia of the following objects are as follows:
1) For a rod:
The moment of inertia of a rod about an axis perpendicular to the length and passing through its center can be calculated using the formula:
I = (1/12) * M * L^2
where I is the moment of inertia, M is the mass of the rod, and L is the length of the rod.
2) For a rectangular plate:
The moment of inertia of a rectangular plate about an axis passing through its center and parallel to one of its sides can be calculated using the formula:
I = (1/12) * M * (a^2 + b^2)
where I is the moment of inertia, M is the mass of the plate, and a and b are the lengths of the sides of the plate.
3) For a ring:
The moment of inertia of a ring about an axis passing through its center and perpendicular to its plane can be calculated using the formula:
I = M * R^2
where I is the moment of inertia, M is the mass of the ring, and R is the radius of the ring.
4) For a circular disc:
The moment of inertia of a circular disc about an axis passing through its center and perpendicular to its plane can be calculated using the formula:
I = (1/4) * M * R^2
where I is the moment of inertia, M is the mass of the disc, and R is the radius of the disc.
To calculate the moment of inertia for any object, you need to know its mass and the dimensions related to the rotational axis. Plug in the appropriate values into the respective formulas to get the moment of inertia for each object.