Question

derive and expression for moment of inertia​

Answer 1

Explanation:

Derivation of the Moment of Inertia Formula

T = F r = m r a . Finally, we use the equation derived about, to convert from linear acceleration to angular acceleration: T = m r a = m r (A r ).

Answer 2

Answer:

Moment of Inertia Formula

In General form Moment of Inertia is expressed as I = m × r2

where,

m = Sum of the product of the mass.

r = Distance from the axis of the rotation.

and, Integral form: I = ∫dI = ∫[0→M] r2 dm

⇒ The dimensional formula of the moment of inertia is given by, M1 L2 T0.

The role of the moment of inertia is the same as the role of mass in linear motion. It is the measurement of the resistance of a body to a change in its rotational motion. It is constant for a particular rigid frame and a specific axis of rotation.

Moment of inertia, I = ∑mi ri2. . . . . . . (1)

Kinetic Energy, K = ½ I ω2 . . . . . . . . . (2)