The formula for moment of inertia for a circle is the product of pi over four times the radius to the power of four. The area moment of inertia is also called the second moment of area. In mathematical notation, the moment of inertia is often symbolized by I, and the radius is symbolized by r.
Unit of Moment Of InertiaMoment of inertia from a Physics point of view is basically a quantitative measure of the rotational inertia or the angular mass of a body. In simple terms, it is the opposition that the body exhibits to the change in rotation about an axis which may further be internal or external.The moment of inertia (I) is mostly specified based on the distribution of mass in the body with respect to the axis of rotation.
Moment of Inertia UnitsFollowing are the two types of moment of inertia with their formula:. Area moment of inertia: mm 4 or in 4. Mass moment of inertia: kg.m 2 or ft.lb.s 2Dimensional Formula: M 1L 2T 0 What is the SI Unit of Moment of Inertia?The SI unit of moment of inertia is: kg.m 2Interested to learn about units of other Physics quantities, below is the link:.Moment Of Inertia Of Rigid BodyFollowing are the moment of inertia for rigid objects.
M 2g.cm 2lb m ft 2lb m in 2kg. M 211×10 72.37×103.42×10 3g.cm 21×10 -712.37×10 -63.42×10 -4lb m ft 24.21×10 -24.21×10 511.44×10 2lb m in 22.93×10 -42.93×10 36.94×10 -31Example of Moment of InertiaConsider a wheel and a uniform disc, both having the same mass rotating about the same axis.
If you may have observed, it is difficult to start or stop the wheel than it is to start or stop the uniform disc.Why is this so, in spite of both the objects having the same mass?This is because the force required to stop a rotating object is directly proportional to the product of the mass and the square of the distance from the axis of rotation to the particles that make up the body.Mathematically, it is represented as F = mr 2In this case, the mr 2 of the wheel mr 2 of the disc.This explains why it is difficult to rotate a wheel compared to a uniform disc.
I = π R 4 / 8How To Find The Moment Of Inertia Of A SemicircleIn order to find the moment of inertia of a semicircle, we need to recall the concept of deriving the moment of inertia of a circle. The concept can be used to easily determine the.1.