学 m=m1+m2+m3+…+mn=∑m m= m,+ma+m, cosa=., cos B=", cosy=m 显然空间力偶系的平衡条件是: m=∑m1=0 投影式为: ∑2=0 =0 M=0 26
26 = = + + + + = n i m m m m mn mi 1 1 2 3 投影式为： mx =0 my =0 mz =0 m m m m m m m m m m x y z = x + y + z ;cos= ,cos = ,cosg = 2 2 2 = =0 m mi 显然空间力偶系的平衡条件是：
Statics 8 5-3 The moment of a force about a point or an axis 1. The moment of a force about a point B3 In the plane it is an algebraic quantity In space, it is a vector EXample] the spherical hinges on the reflective mirror of a car I B 而(F)=Fd=2aa(∠AOB) If r is the radius vector at point A then 27
27 In the plane it is an algebraic quantity. In space, it is a vector. [Example] the spherical hinges on the reflective mirror of a car §5–3 The moment of a force about a point or an axis 1. The moment of a force about a point m (F) F d 2 area( AOB) O = = If r is the radius vector at point A then
学 §5-3力对点的矩与力对轴的矩 力对点的矩的矢量表示 B3 在平面中:力对点的矩是代数量 在空间中:力对点的矩是矢量。 「例]汽车反镜的球铰链 I B 而(F)=Fd=2∠AOB面积 如果r表示A点的矢径,则: 28
28 在平面中：力对点的矩是代数量。 在空间中：力对点的矩是矢量。 [例] 汽车反镜的球铰链 §5-3 力对点的矩与力对轴的矩 一、力对点的矩的矢量表示 mO (F ) =Fd =2AOB面积 如果r 表示A点的矢径，则：
Statics m(F)一F×()刚列F)=Fd The moment of the force about the point o is equal to the vector product of the radius vector of the force at the point and the force. he angle between the two vectors is ∠1=∠2 Because F=Xi+Yj+Zk and r=xi+yj+zk m(F)=F×F=xyz =(yZ-zY )i(EX-xZ)j+(xr-yr)k X Y Z 29
29 The moment of the force about the point o is equal to the vector product of the radius vector of the force at the point and the force. mO (F)=rF,mO (F) = rF sin(r,F)= F d 1=2 Because F = Xi +Yj + Zk and r =xi + yj+zk X Y Z x y z i j k mO (F )=rF = m F i m F j m F k yZ zY i zX x Z j x Y yX k O x O y O z [ ( )] [ ( )] [ ( )] ( ) ( ) ( ) = + + = − + − + − The angle between the two vectors is O
学 m(F)一F×()刚列F)=Fd 即:力对点的矩等于矩心到该力 作用点的矢径与该力的矢量积。 两矢量夹角为=∠2 由于F=X+Y+ZF=x1+y+h m0(F)=×F=xy2=(yz)+(X-x2)+(x-y)k xYz元(F2+m(Fm(F儿k
30 即：力对点的矩等于矩心到该力 作用点的矢径与该力的矢量积。 mO (F)=rF,mO (F) = rF sin(r,F)= F d 1=2 由于F =Xi +Yj+Zk r =xi + yj+zk X Y Z x y z i j k mO (F )=rF = m F i m F j m F k yZ zY i zX x Z j x Y yX k O x O y O z [ ( )] [ ( )] [ ( )] ( ) ( ) ( ) = + + = − + − + − 两矢量夹角为 O