Theoretical mechanics Review o part i statics
1 Theoretical Mechanics
理论力学 静力学复习
2
Statics Review of statics 1. The basic concepts and the difference between them (The difference between a resultant R and the principal vector R: Resultant force R is the sum of the translational effect of the principal vector and the rotational effect of the principal moment(principal vector and principal moment reduce to a resultant force). (It depends on the point of application Principal vector R'only causes only a translational effect Additionally a principal moment may exist. (it does not depend on the point of application 2The difference between a force moment and a force couple moment Force moment is the moment of a force about a point, it depends on the center point. Thereby, it can not be transferred arbitrarily in a plane an Force couple moment can be transfered freely in the plane or in another plane which is parallel to the plane. It does not depend on the center point
3 1. The basic concepts and the difference between them: ①The difference between a resultant R and the principal vector R'. Resultant force R is the sum of the translational effect of the principal vector and the rotational effect of the principal moment (principal vector and principal moment reduce to a resultant force). (It depends on the point of application) Principal vector R' only causes only a translational effect. Additionally a principal moment may exist. (it does not depend on the point of application) ②The difference between a force moment and a force couple moment Force moment is the moment of a force about a point, it depends on the center point. Thereby, it can not be transferred arbitrarily in a plane. Force couple moment can be transfered freely in the plane or in another plane which is parallel to the plane. It does not depend on the center point. Review of Statics
学 静力学复习 基本概念及概念的区分 ①合力R和主矢R的区别 合力R:是主矢的移动效果和主矩转动效果之和(主矢,主矩可 j化为合力)。(与作用点有关) 主矢R:只代表移动效果,且有主矩存在时(与作用点无关) ②力矩和力偶矩的区别 力矩:是力对那一点的转矩,与取矩点有关,且不能在平面内 任意移动。 力偶矩:它是在平面内和平行它自身平面内可任意移动,与取矩 点无关
4 一. 基本概念及概念的区分 ① 合力R 和主矢 R' 的区别 合力R : 是主矢的移动效果和主矩转动效果之和 (主矢,主矩可 简化为合力)。 (与作用点有关) 主矢R': 只代表移动效果，且有主矩存在时(与作用点无关) ② 力矩和力偶矩的区别： 力矩:是力对那一点的转矩, 与取矩点有关, 且不能在平面内 任意移动。 力偶矩: 它是在平面内和平行它自身平面内可任意移动,与取矩 点无关。 静力学复习
Statics @The invariants of the reduction of a general coplanar force system to RER R a given center The invariants of the reduction of a general force system in space to a given center are R in a plane: R In space: R ,=(RR (4) The way to judge the direction of the force of friction Force of friction is a sort of constraint reaction force Its direction is always opposite to the relative motion of the bodies
5 ③The invariants of the reduction of a general coplanar force system to a given center. The invariants of the reduction of a general force system in space to a given center are in a plane: in space: R' // R' ; M M =(R R) ⊥ , ④ The way to judge the direction of the force of friction: Force of Friction is a sort of constraint reaction force. Its direction is always opposite to the relative motion of the bodies.
学 ③平面任意力系向某点简化的不变量, RER R 空间任意力系向某点简化的不变量 平面中:R 空间中:R,MM1=(R,R”) R ④摩擦力的方向判定 摩擦力是一种约束反力,方向总是与物体相对运动方向(趋势 方向)相反
6 ③平面任意力系向某点简化的不变量, 空间任意力系向某点简化的不变量 平面中： 空间中： R' // R' ; M M =(R R) ⊥ , ④摩擦力的方向判定 摩擦力是一种约束反力,方向总是与物体相对运动方向(趋势 方向)相反
Statics Example A running car a braking car The back wheel has driving moment. The back wheel has no driving moment If the back wheel leaves the ground If the back wheel leaves the ground the direction of motion is backward. the direction of motion is forward 7
7 [Example] The back wheel has driving moment. The back wheel has no driving moment. If the back wheel leaves the ground If the back wheel leaves the ground the direction of motion is backward. the direction of motion is forward. A running car A braking car
学 「例] 行驶的汽车 汽车刹车一 后轮有主动力矩,后轮离地后轮无主动力,后轮离地 运动方向是向后的 运动方向是向前的
8 [例] 后轮有主动力矩，后轮离地 后轮无主动力，后轮离地 运动方向是向后的 运动方向是向前的
Statics 5The way to deal with sign of inequality in problems with friction NF. But in general, we only consider the conditions when the motion is impending(.e, NfF), and then append a sign of inequality on the result or judge the range of equilibrium. Therefore we can avoid troubles and miscalculations which would occur in solving inequations 2. Basic equations and theories (1)Basic theories(in common use) O Three coplanar equivalent forces must intersect at one point (to determine the direction of the unknown forces 2 The law of projection of the resultant force: REX The law of the moment of a resultant force: mo(R)=> m o(F7) projection equation m(r)=2m(Fi)
9 ⑤The way to deal with sign of inequality in problems with friction: ∵Nf≥F. But in general, we only consider the conditions when the motion is impending (i.e., Nf=F ), and then append a sign of inequality on the result or judge the range of equilibrium. Therefore we can avoid troubles and miscalculations which would occur in solving inequations. (1) Basic theories (in common use) ① Three coplanar equivalent forces must intersect at one point. (to determine the direction of the unknown forces) ② The law of projection of the resultant force: RX =X ③ The law of the moment of a resultant force: projection equation: ( )= ( ) mO R mO Fi ( )= ( ) mz R mz Fi 2. Basic equations and theories:
学 ⑤摩擦问题中对不等号的处理 N≌F,但一般的情况下是选临界状态代入(即N=F)计 算,得出结果后再加上不等号,或判断出平衡区间,以减少不 等式运算所带来的麻烦和由此出现的误算。 、基本方程和基本定理 ().基本定理(常用的) ①三力平衡必汇交,必共面(用于确定未知力的方向) ②合力投影定理:R=∑X ③合力矩定理:m0(R)=∑m(F) 投影式:m2(R)=∑m2(F1) 10
10 ⑤ 摩擦问题中对不等号的处理 ∵Nf≥F，但一般的情况下是选临界状态代入( 即Nf=F ) 计 算，得出结果后再加上不等号，或判断出平衡区间，以减少不 等式运算所带来的麻烦和由此出现的误算。 (一). 基本定理(常用的) ①三力平衡必汇交，必共面(用于确定未知力的方向) ②合力投影定理：RX =X ③合力矩定理： 投影式： ( )= ( ) mO R mO Fi ( )= ( ) mz R mz Fi 二、基本方程和基本定理