Moment of inertia lecture notes pdf

In the figure below, the two cylinders have the same masses. The smallest moment of inertia about any axis passes through the centroid. It will not attempt to teach you the calculus involved since you are presumed to have learned it in another course. Mass moment of inertia and area moment of inertia duration. Nov 15, 20 the moment of inertia is a geometrical property of a beam and depends on a reference axis. Moments of inertia of geometric areas frame 281 introduction this unit will deal with the computation of second moments, or moments of inertia, of areas. Mass is an intrinsic property of an object, or system of objects. The letter i is a standard notation for moment of inertia.

Lecture 2 spring under impact loading and numerical examples. Axial load, axial torque, strain energy in spring, numerical examples. Compute the moments of inertia of the bounding rectangle and halfcircle with respect to the x axis. Physics 111 lecture 09 rotation, moment of inertia sj 8th ed chap 10. Moment of inertia 5 an example of this is the concrete tbeam shown. The more mass something has, the more it resists acceleration. Lecture notes, lecture 11 center of gravity, centroid and moment of inertia. The moment of inertia, i, of a beam depends on the geometrical properties of the crosssection area a of a beam. The moment of inertia about an axis of a body is calculated by the summation of mr 2 for every particle in the body, where m is the mass of the particle and r is the perpendicular distance from the axis. What is the moment of inertia of the threeobject system. However, if we found the moment of inertia of each section about some.

If this first moment of area is again multiplied by the perpendicular distance between them, the product is known as. The transverse loads cause internal shear forces and bending moments in the beams as shown in figure 1 below. Thisclassisusuallyreferredtoasstatics,butwellbecoveringsomeextra. Lecture 12 moment of inertia lecture 12 moment of inertia. I is relative to the centroid of the crosssection area more generally moment of inertia is defined as i zz. Centre of gravity it is defined as the point through which whole weight of body supposed to be act. Introductory moment of inertia example problem example.

This is known as the parallel axis theorem 24 examples of moment of inertia. This section provides the lecture notes for the course, information on lecture topics, and question posed to the class to stimulate discussion. Calculate first and second moment of area of simple geometry. Lecture notes on engineering mechanics properties of area, first and second moments of area or inertia, transformation, mohrs circle diagram. However, the cylinder with larger diameter will have greater moment of inertia larger lever 825 arm than the one with smaller. The particular skills you will need are in establishing. Integral represent the moment of inertia of area about the y axis. Lecture notes physics i physics mit opencourseware.

Viken kiledjian gives the definition and meaning of moment of inertia and how to find the moment of inertia of 1 or more objects around any axis. Lecture 1 introduction, units, linear algebra 0introduction welcometoengineeringmechanicsi. For a point mass, m, the moment of inertia about the line is. View notes lecture 12 moment of inertia from ph 1011 at nanyang technological university. Welcome to lecture summary 5a, which will concentrate on centroid and moments of inertia of cross sectional shape of members. It is defined as the point through which whole area is assumed to be concentrated. N i mi ri 2 i 1 two spheres a spun baton has a moment of inertia due to each separate mass. The moment of inertia of the shaded area is obtained by subtracting the moment of inertia of the halfcircle from the moment of inertia of the. Notes on torque weve seen that if we define torque as rfsin.

Pdf ge8292 engineering mechanics lecture notes, books. Mass moment of inertia, i g contd i g for a body depends on the bodys mass and the location of the mass. The moment of inertia of the area about the yaxis and the radius of gyration ky. The centroid, or center of gravity, of any object is the point within that object from which the force of gravity. Polar moment of inertia moment of inertia about the z axis the polar area moment of inertia of a beams crosssectional area measures the beams ability to resist torsion. It tells us how difficult is to set an object in rotational motion.

Here the quantity i is called the objects moment of inertia. The polar moment of inertia is the sum of any two moments of inertia about axes at right angles to each other, e. The moment of inertia of a composite area a about a given axis is obtained by. Although it is a simple matter to determine the moment of inertia of each rectangular section that makes up the beam, they will not reference the same axis, thus cannot be added. The greater the distance the mass is from the axis of rotation, the larger i g will be. Assume we have an extended body rotating about some. The inertia tensor we found last time that the kinetic energy and angular momentumof a rotating object were. Change in rotation from torque moment of inertia i mr2 for a single mass the total moment of inertia is due to the sum of masses at a distance from the axis of rotation. The moment of inertia measures the resistance to a change in rotation.

Determine the moment of inertia of the shaded area with respect to the x axis. Every year there are questions asked from this topic. Here, the moment of inertia iplays the same role as the objects mass min f ma. Of a body about an axis is the sum of the products of its mass elements and the squares of their distances to the axis. System of particle and rotational motion is an important topic from jee main jee advanced exam point of view. The polar moment of inertia j of an element about an axis perpendicular to its plane is the product of the area of the element and the square.

In civil engineering, it is often combined this geometric property with material properties to determine physical quantities such as stiffness. Physics 111 lecture 09 rotation, moment of inertia sj 8th ed. If we have a distributed mass we compute the moment of inertia by summing the contribu tions of each of its parts. The moment of inertia, also known as the second moment of area, is basically a geometric property related to some object resistance to rotational movements. Pdf lecture notes on engineering mechanics properties of area. Lecture series on strength of materials5 moment of inertia. The moment of inertia mi of a plane area about an axis normal to the plane is equal to the sum of the moments of inertia about any two mutually perpendicular axes lying in the plane and passing through the given axis. The moment of inertia about any point or axis is the product of the area and the perpendicular distance between the point or axis to the centre of gravity of the area. For example, flywheels have a heavy outer flange that locates as much mass as possible at a greater distance from the hub. I m i r i 2 when the distribution of mass is continuous, the discrete sum becomes. Moment of inertia ph1011 physics week 6 lecture 12. Lecture 11 deflection in beams by moment area method lecture 12 numerical examples on deflection of beams by moment area method module 4 lecture 1 closed coiled helical springs.