Inerces moments ir inerces m?rs rot?cijas kust?bai. Rot?cijas kust?b? ?erme?a inerce nav atkar?ga tikai no t? masas , bet ar? no att?luma l?dz rot?cijas asij.

Liels inerces moments piem?t cilindrisk?m ?aul?m, t?d? form? ir, piem?ram, spararati , lai uzkr?tu griezes kust?bas ener?iju un l?dzsvarotu rot?cijas kust?bu.

Matem?tiskais pieraksts [ labot ?o sada?u | labot pirmkodu ]

Inerces momentu var apr??in?t k? katra materi?la punkta inerces momentu, kas ir t? masas reizin?jums ar att?luma l?dz rot?cijas asij kvadr?tu:

${\displaystyle I=mr^{2}}$, kur ${\displaystyle I}$-inerces moments; ${\displaystyle m}$- masa; ${\displaystyle r^{2}}$-att?lums l?dz rot?cijas asij. ^[1]

Visp?r?g? gad?jum?, ja ir zin?ms ?erme?a bl?vums , inerces momentu var pierakst?t k? integr?li : ${\displaystyle I=\int _{V}\rho r^{2}dV}$, kur ${\displaystyle \rho V}$- masa maz? tilpum? , ${\displaystyle r^{2}}$-att?lums l?dz rot?cijas asij. ^[2]

Inerces momentu var saist?t ar? ar impulsa momentu un le??isko ?trumu : ${\displaystyle I={\frac {L}{\omega }}}$.

Inerces momenti da??d?m form?m [ labot ?o sada?u | labot pirmkodu ]

?ermeni nevar uzskat?t par masas punktu, jo vienam ?ermenim var b?t da??di inerces momenti atkar?b? no rot?cijas ass izv?les. Lai ieg?tu ?erme?a inerces momentu, ir j?saskaita visu ?erme?a punktu inerces momenti: ${\displaystyle I=\sum _{i=1}^{N}m_{i}r_{i}^{2}}$

Inerces moments cilindram [ labot ?o sada?u | labot pirmkodu ]

Inerces momenta formula cilindram ir: ${\displaystyle I={\frac {1}{2}}mr^{2}}$.

Ja cilindrs ir homog?ns un t? bl?vums ir ${\displaystyle \rho }$, tad ${\displaystyle dm=\rho dV=\rho h2\pi rdr}$ - tikai cilindra r?diuss . ${\displaystyle r}$ ir vien?gais cilindra tilpuma parametrs, kur? maina masas att?lumu no rot?cijas ass.

Saska?? ar formulu ${\displaystyle I=\int _{V}\rho r^{2}dV=2\pi \rho h\int _{R}r^{3}dr}$, integr?jot robe??s ${\displaystyle [0;R]}$ ieg?st ${\displaystyle I={\frac {1}{2}}\pi h\rho r^{4}}$, t? k? cilindra tilpums ir ${\displaystyle \pi r^{2}h}$, tad t? masa ir ${\displaystyle \pi r^{2}h\rho }$ un inerces moments ir ${\displaystyle I={\frac {1}{2}}mr^{2}}$. ^[3]

Atsauces [ labot ?o sada?u | labot pirmkodu ]

1. ↑ Fizmix. ≪Fizikas t?ma - Inerces moments≫ . Fizmix (latvie?u) . Skat?ts: 2023-11-13 .
2. ↑ ≪Fizikas rokasgr?mata≫ . gramatas.lndb.lv . 1988.gads. 87.?88. lpp . Skat?ts: 2023-11-13 .
3. ↑ ≪1.3. Cieta ?erme?a dinamika≫ . estudijas.rtu.lv . 3.?4. lpp . Skat?ts: 2023-11-14 .