2022-2023學(xué)年高二物理競(jìng)賽課件：力對(duì)點(diǎn)的矩和力對(duì)軸的矩

力對(duì)點(diǎn)的矩和力對(duì)軸的矩

(MomentofForceaboutaPointandanAxis)力對(duì)點(diǎn)的矩和力對(duì)軸的矩

(MomentofForceaboutaPointandanAxis)一、力對(duì)點(diǎn)的矩以矢量表示上式為力對(duì)點(diǎn)的矩的矢積表達(dá)式。力矩矢不可任意挪動(dòng)，稱(chēng)為定位矢量。

力矩矢在三個(gè)坐標(biāo)軸上的投影FzFxFy力對(duì)點(diǎn)的矩和力對(duì)軸的矩

(MomentofForceaboutaPointandanAxis)定義:力使物體繞某一軸轉(zhuǎn)動(dòng)效應(yīng)的量度,稱(chēng)為力對(duì)該軸之矩.

二、力對(duì)軸的矩當(dāng)力與軸在同一平面時(shí)，力對(duì)軸無(wú)轉(zhuǎn)動(dòng)效應(yīng)。這兩種情況合起來(lái)說(shuō)：當(dāng)力與軸在同一平面時(shí)，力對(duì)軸的矩等于零。力對(duì)于任一軸的矩，等于力在垂直該軸平面上的投影對(duì)于軸與平面的交點(diǎn)的矩。力對(duì)軸的矩等于零的情況：（1）當(dāng)力與軸相交時(shí)（此時(shí)h=0）；（2）當(dāng)力與軸平行時(shí)（此時(shí)Fxy=0）。力對(duì)軸的矩的單位：N?m。力對(duì)點(diǎn)的矩和力對(duì)軸的矩

(MomentofForceaboutaPointandanAxis)力對(duì)點(diǎn)的矩和力對(duì)軸的矩

(MomentofForceaboutaPointandanAxis)

正負(fù)號(hào)規(guī)定：從z軸的正向看，逆時(shí)針的矩取正號(hào)，反之取負(fù)號(hào)。右手螺旋法則力對(duì)軸的矩的解析表達(dá)式：即同理可得其余二式。將此三式合寫(xiě)為力對(duì)點(diǎn)的矩和力對(duì)軸的矩

(MomentofForceaboutaPointandanAxis)三、力對(duì)點(diǎn)的矩與力對(duì)通過(guò)該點(diǎn)的軸的矩的關(guān)系比較前面兩式，可得上式說(shuō)明：力對(duì)點(diǎn)的矩矢在通過(guò)該點(diǎn)的某軸上的投影，等于力對(duì)該軸的矩。

如果已知力對(duì)通過(guò)點(diǎn)O的直角坐標(biāo)軸x，y，z的矩則可求得該力對(duì)點(diǎn)O的矩的大小和方向余弦為力對(duì)點(diǎn)的矩和力對(duì)軸的矩

(MomentofForceaboutaPointandanAxis)例：傳動(dòng)軸上圓柱斜齒輪所受的嚙合力為F,齒輪壓力角為α,螺旋角為β,節(jié)圓半徑為r。求該力對(duì)于各坐標(biāo)軸的矩。解：嚙合力F沿坐標(biāo)軸分解力作用點(diǎn)的坐標(biāo)為:代入公式，得:FxFyFz力對(duì)點(diǎn)的矩和力對(duì)軸的矩

(MomentofForceaboutaPointandanAxis)嚙合力F在軸上的投影為:力對(duì)點(diǎn)的矩和力對(duì)軸的矩

(MomentofForceaboutaPointandanAxis)方法二:將力向三個(gè)坐標(biāo)軸方向分解,分別求三個(gè)分力對(duì)軸之矩，然后將三個(gè)分力對(duì)軸之矩的代數(shù)值相加。FxFyFz力對(duì)點(diǎn)的矩和力對(duì)軸的矩

(MomentofForceaboutaPointandanAxis)[例]已知:P=2000N,C點(diǎn)在Oxy平面內(nèi)求：力P對(duì)三個(gè)坐標(biāo)軸的矩解：將P力進(jìn)行分解，各分力的大小為：力對(duì)點(diǎn)的矩和力對(duì)軸的矩

(MomentofForceaboutaPointandanAxis)四、空間力偶

實(shí)際經(jīng)驗(yàn)告訴我們：力偶的作用面可以平行移動(dòng)，而不改變力偶對(duì)剛體