Jaký je rozdíl mezi momentem hybnosti a rotační setrvačností? Jaké jsou jejich podobnosti?


Odpověď 1:

Itssimilartothedifferencebetweenmassandmomentum.Theequationforlinearmomentumisp=mv.Momentumisafunctionofmass(wheretheinertiacomesfrom)andthevelocity.Thenicethingaboutrotation,isthatmanyrotationalquantitiesareanalogsoflinearquantities.Angularmomentum[math]L[/math]istheanalogueoflinearmomentumandrotationalinertia[math]I[/math]istheanalogueofmass.Itwouldmakesincethenthatangularmomentumandrotationalinertiaarerelatedbytheangularanalogueofvelocityandindeedtheyare!Angularmomentumequalsrotationalinertiatimesangularvelocity[math]ω[/math]or[math]L=Iω[/math].It's similar to the difference between mass and momentum. The equation for linear momentum is p=mv. Momentum is a function of mass (where the inertia comes from) and the velocity. The nice thing about rotation, is that many rotational quantities are analogs of linear quantities. Angular momentum [math]L[/math] is the analogue of linear momentum and rotational inertia [math]I[/math] is the analogue of mass. It would make since then that angular momentum and rotational inertia are related by the angular analogue of velocity and indeed they are! Angular momentum equals rotational inertia times *angular velocity [math]ω[/math] or [math]L=Iω[/math].

angularvelocity(rateofchangeofanangle)isrelatedtolinearvelocitybytherelation:v=ωrwhere[math]r[/math]istheradiusofapointrotatingand[math]v[/math]isthevelocityofthatpoint.*angular velocity (rate of change of an angle) is related to linear velocity by the relation: v=ωr where [math]r[/math] is the radius of a point rotating and [math]v[/math] is the velocity of that point.