State the expression for moment of inertial of the following (1)A rod (2) Rectangular plate (3) ring (4) circular disc
To state the expressions for the moments of inertia of different objects, let's consider the following:
1) A Rod:
The moment of inertia of a rod rotating about an axis perpendicular to its length can be calculated using the formula:
I = (1/12) * m * L^2,
Where:
I - Moment of inertia
m - Mass of the rod
L - Length of the rod
2) Rectangular Plate:
The moment of inertia of a rectangular plate rotating about an axis perpendicular to its plane can be calculated using the formula:
I = (1/12) * m * (a^2 + b^2),
Where:
I - Moment of inertia
m - Mass of the rectangular plate
a - Length of one side of the rectangle
b - Length of the adjacent side of the rectangle
3) Ring:
The moment of inertia of a ring rotating about an axis passing through its center and perpendicular to its plane can be calculated using the formula:
I = m * r^2,
Where:
I - Moment of inertia
m - Mass of the ring
r - Radius of the ring
4) Circular Disc:
The moment of inertia of a circular disc rotating 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 - Moment of inertia
m - Mass of the circular disc
R - Radius of the circular disc
These formulas provide the expressions for the moments of inertia of the mentioned objects.