Kinematics Conclusions: 2. Features of translational motion: All the particles of a rigid body with translational motion have the same motion, i. e. their trajectories, velocities and accelerations are identical The translation of a rigid body can be simplified to the motion of a particle in it
11 Conclusions: 2. Features of translational motion: All the particles of a rigid body with translational motion have the same motion, i. e. their trajectories, velocities and accelerations are identical. The translation of a rigid body can be simplified to the motion of a particle in it
动学 得出结论:即 二刚体平动的特点: 平动刚体在任一瞬时各点的运动轨迹形状,速度加速度都 样。 即:平动刚体的运动可以简化为一个点的运动。 12
12 得出结论:即 二.刚体平动的特点: 平动刚体在任一瞬时各点的运动轨迹形状,速度,加速度都一 样。 即:平动刚体的运动可以简化为一个点的运动
Kinematics 87-2 Rotation of a rigid body about a fixed axis 1. Feature of rotation about a fixed axis and its simplification Feature: There is a fixed line called axis, and every point of the rigid body which is not on this axis moves along a circular path in a plane perpendicular to this fixed axis 2. Angle of rotation and equation of rotation o--- angle of rotation, whose unit is rad o-f(o---equation of rotation Sign definition: follows right-hand rule counter-clockwise clockwise
13 §7-2 Rotation of a rigid body about a fixed axis 1. Feature of rotation about a fixed axis and its simplification Feature :There is a fixed line called axis, and every point of the rigid body which is not on this axis moves along a circular path in a plane perpendicular to this fixed axis. 2. Angle of rotation and equation of rotation --- angle of rotation,whose unit is rad. =f(t)--- equation of rotation Sign definition: follows right-hand rule. counter-clockwise clockwise
学 §7-2刚体的定轴转动 一.刚体定轴转动的特征及其简化 特点:有一条不变的线称为转轴,其余各点都在垂直于转轴的平 面上做圆周运动。 二.转角和转动方程 q-转角,单位弧度(rad) =f(t)一为转动方程 方向规定:从z轴正向看去, 逆时针为正顺时针为负
14 §7-2 刚体的定轴转动 一.刚体定轴转动的特征及其简化 特点:有一条不变的线称为转轴,其余各点都在垂直于转轴的平 面上做圆周运动。 二.转角和转动方程 ---转角,单位弧度(rad) =f(t)---为转动方程 方向规定: 从z 轴正向看去, 逆时针为正 顺时针为负
Kinematics 3. Angular velocity and angular acceleration o=lim △d "i=o(algebraic quantity) 0△tat (1) Definition of the angular velocity If the equation of the rotation is given as p=fCt) then @=f(t), The unit is rad/s (t+△ Unit used in engineering △(t n=rpm (round per minute) The relation between n and w Is 2rn nn O (rad/s) 603010 15
15 Unit used in engineering: n = rpm (round per minute) The relation between n and w is ) n n n (rad/s 60 30 10 2 = = then = f (t), The unit is rad/s. If the equation of the rotation is given as = f(t) 3. Angular velocity and angular acceleration (1). Definition of the angular velocity： (algebraic quantity) Δ Δ lim Δ 0 = = = → dt d t t