Difference Between Moment of Inertia and Polar Moment of Inertia

Main Difference – Moment of Inertia vs. Polar Moment of Inertia

Moment of inertia (which refers to the mass second moment of inertia) and polar (second) moment of inertia are both quantities which describe an object’s ability to resist changes due to torques applied to it. The main difference between moment of inertia and polar moment of inertia is that the moment of inertia measures how an object resists angular acceleration, whereas the polar moment of inertia measures how an object resists torsion.

What is Moment of Inertia

Moment of inertia for a body is defined with the following integral:

I=\int r^2\:\mathrm dm

where r is the distance of the mass element \mathrm dm from the axis of rotation.

Physically, the moment of inertia gives the ability of a body to resist angular acceleration (analogous to how mass resists linear acceleration) when subject to a torque. If the moment of inertia is large, then the angular acceleration produced by a given torque would be smaller. The unit of moment of inertia is kg m2.

Moment of inertia is used to calculate rotational kinetic energy and also to calculate torque in terms of mass and angular acceleration.

What is Polar Moment of Inertia

Polar second moment of inertia gives an object’s ability to resist torsion (i.e. “twisting”) about a given axis due to an applied torque. If the polar moment of inertia is large, the torsion produced by a given torque would be smaller. Polar moment of inertia is defined as:

I=\int r^2\:\mathrm dA

where r is the distance of the area element \mathrm dA from the axis of rotation. The unit of polar moment of inertia is m4.

Difference Between Moment of Inertia and Polar Moment of Inertia - Calculating Polar Moment of Inertia in 2D

Difference Between Moment of Inertia and Polar Moment of Inertia – Defining Polar Moment of Inertia (here shown in 2D)

Polar second moment of area is often confused with the area second moment of inertia, which is defined:

I=\int x^2\:\mathrm dA

where x is the distance of the area element \mathrm dA from a specific plane.  This also has units of m4, however physically this quantity indicates the resistance of an object to bend about a certain plane when subjected to a torque.

Difference Between Moment of Inertia and Polar Moment of Inertia

Mathematical definition of Moment of Inertia and Polar Moment of Inertia

Moment of inertia is defined as I=\int r^2\:\mathrm dm .

Polar moment of inertia is defined as I=\int r^2\:\mathrm dA .

Physical Meaning

Moment of inertia is a measurement of an object’s resistance to angular acceleration.

Polar moment of inertia is a measurement of an object’s resistance to torsion (twisting).

Units

Moment of inertia is measured in units of kg m2.

Polar moment of inertia is measured in units of m4.

Image courtesy
“A diagram showing the elemental area used in calculating the polar moment of inertia of a flat object.” by Inductiveload (Own work) [Public Domain], via  (Modified)

About the Author: Nipun


Related pages


synesthesia in literaturechromosomes vs chromatidc3 versus c4 plantsagnostic and atheist differencewhat is the difference between alaskan malamute and siberian huskyagnostic oppositethermal conductivity and thermal diffusivityexample of antithesis in poetrycytosine binds withan example of asyndetontheism deismcharacteristics of modern tragedyceramic and electrolytic capacitordistinguish between photosynthesis and respirationembryo zygote fetuscolonialism and imperialismdolphins and sharks factsdefinition of karyokinesisthe difference between dietitian and nutritionistsimilarities and differences between aerobic and anaerobic respirationallude or eludewhat's the difference between bachelors and associates degreewhats foreshadowingexplain the difference between diabetes mellitus and diabetes insipidusaustralian flag stars meaningcpi index formuladefine static characterdifference between intermolecular forces and intramolecular forceswhat is the difference between homogeneous and heterogeneous mixturesdefinition of regular polygonshow does assonance effect a poemmicrofilaments intermediate filaments and microtubulesflagella and piliwhat is the difference between ambassador and high commissionerwhat's foreshadowingwhat is cereals in hindipitbull or bulldogniche hypervolumewhat is the difference between lake and pondmechanism of sn1 and sn2 reactionssugarcane and sugar beetmitosis without cytokinesischaracteristics of interphasedefinition blastocystdefine entendreexamples of amorphous polymersexample of naturalism in literaturegold foil experiment conclusionproton neutronsdifference between formaldehyde and paraformaldehydeprotostomdoctrine and dogmaswan goose differenceenergy band diagram of p type semiconductorhow do you write a cinquain poemwhat is a scallion vs green onionsdifference between turmeric and curcuminis baking soda and bicarbonate soda the same thingwhat does blastula meanbasophils and eosinophilssimple pendulum and compound pendulumfunction of micropyle in seedluminescence vs fluorescencebiannually meanscomedy tragedy definitionbrandy vs whiskey vs bourbondifference between ionic covalent and hydrogen bondssimilarities between balanced and unbalanced forcesis heavy cream and heavy whipping cream the samenovella meaningdifference between esthetician and aestheticianwhat is megaloblastic anemiabaso4 in watereffects of manmade disasters wikipediais celexa better than prozachealth benefits of pecans vs walnutsexample of acculturation in culturevernier caliper precision