第十一章動(dòng)量矩定理習(xí)題解答

1、1習(xí)題111質(zhì)量為m的質(zhì)點(diǎn)在平面Oxy內(nèi)運(yùn)動(dòng)，其運(yùn)動(dòng)方程為：。tbytax??2sincos??其中a、b和w均為常量。試求質(zhì)點(diǎn)對(duì)坐標(biāo)原點(diǎn)O的動(dòng)量矩。taxvx??sin????tbyvy??2cos2???xmvymvLyxO???)cos2cos22sinsin(tatbtbtam??????????)cos2cos22sin(sinttttmab?????????)cos2cos2cossin2(sintttttmab??????

2、????)2cos(sincos22tttmab??????tmab??3cos2?112C、D兩球質(zhì)量均為m，用長(zhǎng)為2l的桿連接，并將其中點(diǎn)固定在軸AB上，桿CD與軸AB的交角為，如圖1125所示。如軸AB以角速度w轉(zhuǎn)動(dòng)，試求下列兩種情況?下，系統(tǒng)對(duì)AB軸的動(dòng)量矩。（1）桿重忽略不計(jì)；（2）桿為均質(zhì)桿，質(zhì)量為2m。圖1125(1)??222sin2)sin(2mllmJz?????22sin2lmLz?(2)??2202sin32d)

3、sin(2mlxxlmJlz???桿?22sin38mlJz???22sin38lmLz?113試求圖1126所示各均質(zhì)物體對(duì)其轉(zhuǎn)軸的動(dòng)量矩。各物體質(zhì)量均為m。圖1126(a)?231mlLO?(b)22291)6(121mllmmlJO????291mlLO??(c)2222452312121mllmlmJO????????2245mlLO?(d)2222321mRmRmRJO????223mRLO?114如圖1127所示，均質(zhì)三角形

4、薄板的質(zhì)量為m，高為h，試求對(duì)底邊的轉(zhuǎn)動(dòng)慣量Jx。321221)4(61amamJC??mmaam16π16π221??22296π325616π2138mamamaJC?????mmmm16π1616π?????222296π48896π3256816π1696π3256)22(mRammaamJJCO??????????????296π511024mR????2961024π51mRJLOO????117如圖1130所示，質(zhì)量為m的

5、偏心輪在水平面上作平面運(yùn)動(dòng)。輪子軸心為A，質(zhì)心為C，AC＝e；輪子半徑為R，對(duì)軸心A的轉(zhuǎn)動(dòng)慣量為JA；C、A、B三點(diǎn)在同一直線上。試求下列兩種情況下輪子的動(dòng)量和對(duì)地面上B點(diǎn)的動(dòng)量矩：(1)當(dāng)輪子只滾不滑時(shí)，已知vA；(2)當(dāng)輪子又滾又滑時(shí)，已知vA、w。圖1130??)()()(2meJeRmvJeRmvLAcCCB?????????(1)RvA???)(eRvC??RveRmmeJRvmeJRveRmLAAAAAB])([)()(22

6、22??????????(2)?evvAC????CABJeRevmL?????))((??)()()(2meJeRmeveRmAA???????])()([?meRJveRmAA?????118曲柄以勻角速度w繞O軸轉(zhuǎn)動(dòng)，通過(guò)連桿AB帶動(dòng)滑塊A與B分別在鉛垂和水平滑道中運(yùn)動(dòng)，如圖1131所示。已知OC＝AC＝BC＝l，曲柄質(zhì)量為m，連桿質(zhì)量為2m，試求系統(tǒng)在圖示位置時(shí)對(duì)O軸的動(dòng)量矩。圖1131(順時(shí)針)???ABABOCOLLL???