Calculate first and second moment of area of simple geometry. Definition polar moment of inertia, transfer theorem, moments of inertia of composite figures, products of inertia, transfer formula for product of inertia. Moment of inertiaof point mass qfor a single particle, the definition of moment of inertia is nm is the mass of the single particle nr is the rotational radius qsi unitsof moment of inertia are kg. Lecture, pg 10 inertia rods two batons have equal mass and length. Area moment of inertia definition, moment of inertia of plane sections from first principles.
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 the resultant about any axis was determined by computing the first moments of the areas or volumes about that axis. The letter i is a standard notation for moment of inertia. The moment of inertia is the mechanical resistance to torque and measures the spatial distribution of mass of an object. This means that moment of inertia or rotational mass is a. Comprehend the action of forces, moments and other loads on systems of rigid bodies. Engineering mechanics pdf notes em notes free lecture. The total moment of rmust equal the total moment of. Express the relationship between the motion of bodies and 6. Integral represent the moment of inertia of area about the y axis. Physics of the earths interior universiteit utrecht. Calculate the moment of inertia of each component about its own horizontal centroidal axis i for vertical or horizontal plateshape breadth b, depth d. Principal axes resolution of bending moment into two rectangular axes through the centroid location of neutral axis 5. Rotational motion angular acceleration rotationaltolinear quantities moment of inertia rotational kinetic energy write these equations in your notes if theyre not already there.
But reading technical material is a skill worth learning, and this seems as good a time as any to start working on it. 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. For a point mass, m, the moment of inertia about the line is. When the system of particles is a continuum, the summation over the number of particles is written as an integral, ig z m r. Moment of inertia only depends on distribution of mass perpendicular to rotation axis, and on the orientation and location of rotation axis rotation about an axis offset from center of mass can. Introduction to security studies lecture notes lecture 1 lecture notes, lecture 5 force vectors lecture notes, lecture 2 general principles lecture notes, lecture 3 force vectors inertia formulas see notice 20172018 autumn. Enr202 mechanics of materials lecture 5a slides and notes. Pdf lecture notes on unit4 centroid,centre of gravity.
Thisclassisusuallyreferredtoasstatics, butwellbecoveringsomeextra material that typically falls into the category of dynamics. Calculate the height of the na above the baseline hna. The more mass something has, the more it resists acceleration. Ancalle updated 12020 the procedure for finding the moment of inertia is quite simple, if you remember how to find a centroid. Moment of inertia formulas, moi of objects solved examples. The moment of inertia measures the resistance to a change in rotation. For example, flywheels have a heavy outer flange that locates as much mass as possible at a greater distance from the hub.
The inertia tensor we found last time that the kinetic energy and angular momentumof a rotating object were. Review and critical analysis of mass and moments of inertia of the lageos and lageos ii satellites for the larase program massimo viscoa,b, david m. Lecture notes on engineering mechanics properties of area, first and second moments of area or inertia, transformation, mohrs circle diagram. Everybody consists of innumerable particles, however the entire weight of a body is assumed to act through a single point and such a single.
Point mass at a radius r thin rod about axis through center perpendicular to length thin rod about axis through end perpendicular to length thinwalled cylinder about. Polar moment of inertia j r2 da the polar moment of inertia is the sum of the produce of each bit of area da and the radial distance to an origin squared. But in mechanics, moment of inertia is used in the. Determine the moment of inertia for the rectangular area with respect to a the centroidal x axis. Phys 3200 lecture notes richard taylor, 2020 1 introduction reading mathematics and physics is a fairly advanced skill. Moment of inertia is not a physical quantity such as velocity, acceleration or force, but it enables ease of calculation. Calculate the moment of inertia of the total section about the baseline ibl. Lecture notes, lecture 11 center of gravity, centroid and. Stresses in beams subject to unsymmetrical bending 4. Most students nd that an interactive lecture format is an easier way to get acquainted with new ideas. Physics 111 lecture 09 rotation, moment of inertia sj 8th ed. Moments of inertia 53 statics lecture notes by david s.
These will be continuously updated over the course of the semester to make the notation more consistent, fill in gaps, and type up the handwritten notes. Compute the reactive forces and the effects that develop as a result of the external loads. Physics 111 lecture 09 rotation, moment of inertia sj 8th ed chap 10. N i mi ri 2 i 1 two spheres a spun baton has a moment of inertia due to each separate mass. Please check out the updated videos on the same content. Which will be easier to spin a mass on ends b same c mass in center i s m r2 further mass is from axis of rotation, greater moment of inertia harder to spin. Chapter 0 introduction welcometoengineeringmechanicsi. Area moments of inertia previously considered distributed forces which were proportional to the area or volume over which they act. A composite area is made by adding or subtracting a series. Graphical method for locating principal axes moments of inertia referred to any set of rectangular axes 3.
Welcome to lecture summary 5a, which will concentrate on centroid and moments of inertia of cross sectional shape of members. Locate the centroid and compute the moment of inertia of regular crosssections. Since in dynamics there is no such concept as the inertia of an area, the moment of inertia has no physical meaning. The resultant was obtained by summing or integrating over the areas or volumes. 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. The force of attraction is proportional to mass of the body. Mass moment of inertia, i g contd i g for a body depends on the bodys mass and the location of the mass. Dec 11, 2020 phy422820 classical mechanics fall semester 2020 these are my lecture notes from fall semester 2019. The total moment of inertia is due to the sum of masses at a distance from the axis of rotation. Moments of inertia of composite areas sample problem 9. Compute the moments of inertia of the bounding rectangle and half. If we have a distributed mass we compute the moment of inertia by summing the contribu tions of each of its parts. Moment of inertia of masses, transfer formula for mass moments of inertia, mass moment of inertia of composite bodies. All formulas shown assume objects of uniform mass density.
Pdf lecture notes on engineering mechanics properties of area. The maximum moment of inertia is known as major principal moment of inertia and the minimum moment of inertia is known as minor principal moment of inertia. Among two values of moments of inertia about the set of principal axes. A collection of two masses has a moment of ine rtia due to each separate mass. Compute the moments of inertia of the bounding rectangle and halfcircle with respect to the x axis. Chapter 4 slope deflection method and moment distribution method introduction continuous beams clapeyrons theorem of three moments analysis of continuous beams with constant variable moments of inertia with on e or both ends fixed continuous beams with overhang effects of sinking of supports derivation of slope deflection equation. Be able to compute the moments of inertia of composite areas. If this body is also rotating about one of its principal axis, say, the z, then. The greater the distance the mass is from the axis of rotation, the larger i g will be. Determine the moment of inertia of the shaded area with respect to the x axis.
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