Question

state and explain principle of moment of inertia of rotationalequbilirium

Answer 1

A rigid body is considered to be in equilibrium, if there is:

Translational equilibrium; AND

Rotational Equilibrium.

A body in equilibrium experiences NO acceleration and will remain in equilibrium indefinitely, UNLESS it is disturbed by an external force. (Newton’s First Law)

Translational equilibrium is obtained when the resultant force or vector sum of all forces acting upon the rigid body is zero. In simpler terms, this means that:

forces pointing to left = forces pointing to right; AND

forces pointing up = forces pointing down

Principle Of Moments

Rotational equilibrium is obtained when the algebraic sum of the torques is zero.

However, it can also be interpreted as:

The principle of moments states that for a body to be in rotational equilibrium, the sum of clockwise torques about any point (which acts as a pivot) must equal to the sum of anti-clockwise torques about the same point.

Answer 2

$\huge\bold\red{ANSWER:-}$

First let me give you an intuitive explanation on MOMENT OF INERTIA (will be referring to as MOI)

consider a solid disc of radius 'R' of certain mass rotating about its own axis passing through the center

Now consider a solid sphere of same mass rotating at a distance same as radius 'R' of the disc.

(Both the cases have a moderate speed.)

If you try stopping these two rotating bodies,you will be able to stop the solid disc easily compared to that of the solid sphere. Stopping the solid sphere requires a significant effort.

Inference-MOI of the latter case is very high compared to the first case.

MOI is used to measure or quantify the mass situated at the extremities of an object.

◆ Few applications of MOI-

FLYWHEEL of an automobile. Flywheel is a heavy mass mounted on the crankshaft of an engine. The magnitude of MOI of the flywheel is very high and helps in storing the energy.

◆ Hollow shaft- An hollow

shaft transmits more power compared to that of a solid shaft(both of same mass). The MOI of hollow shaft is more compared to that of a solid shaft. ( In a way, the mass at the center of solid shaft is removed and is stacked at the periphery and hence increasing its moment of inertia).

◆ Shipbuilding- MOI has a big impact on shipbuilding. A ship may sink by rolling but a ship will never sink by pitching. The reason is, the MOI over pitching axis is significantly huge compared to that over rolling axis. In battleships the MOI inertia is high in order to reduce the time period of oscillation as a result of any disturbance.

In the above application the MOI is increased by just placing the significant amount mass away from the axis of rotation or oscillation.

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