质点运动的几种典型形式.ppt

一、匀速直线运动（straight line motion with constant velocity）,(常数),二、匀加速直线运动（straight line motion with constant acceleration）,(常数),自由落体运动（freely falling bodies）,三、抛体运动（projectile motion）,Path equation：,由于空气阻力，实际射程小于最大射程,求最大射程,当,END,四、圆周运动（ circular motion）,1. Angular variables(角量） in circular motion, Angular position,Position function,Angular displacement,Direction: defined in the direction of advance of a right-handed screw,Caution,A finite angular displacement is not a vector, an infinite angular displacement is!,Reason：,(disobey the Commutative law), angular velocity & angular acceleration,角速度：,角加速度：,Counterclockwise(逆时针）: positive direction Clockwise（顺时针） : negative direction,Two directions:,2.The intrinsic coordinate system（自然坐标系）,Two unit vector are introduced to describe the circular motion:,is an unit vector tangent (相切)to the circle at A directing to the advance direction and an unit vector is normal to the circle at a （法向 ） directing toward the center O.,Hence(所以）, the acceleration of particle is :,(1-23),Obviously（显然）, we have,Using and , the velocity can be expressed as（表示成）:,(1-24).,It is easy to prove the rate of the tangential unit vector to be equal to,t,o,t+t,Prove: when , we have,To summarize（总结）, we have,and are called the tangential acceleration（切向加速度） and normal acceleration（法向加速度） respectively, and their magnitudes are given by,Angle :,Magnitude of :,Changes the magnitude of the velocity;,Changes the direction of the velocity.,3. Relation between linear（线） & angular variables：,4. Uniform circular motion(匀速圆周运动）,v=const,5.General curvilinear motion:,(1-30),=AC is the radius of curvature（曲率） at A and C is the center of curvature circle (曲率圆）.,A small part of curvilinear path can be considered as a part of a circle as shown in the below figure. We have,Example: 一质点沿半径为R 的圆周按,规律运动，V0, b 是正值常