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,Click to edit Master title style,Click to edit Master text styles,Second Level,Third Level,Fourth Level,Fifth Level,#,t,e,d,=,q,d,n,e,=,t,e,d,t,d,d,t,d,q,n,e,=,d,t,d,q,n,e,R,R,(,),=,d,t,d,R,s,1,n,e,=,R,v,n,e,a,+,t,e,v,=,d,t,d,R,v,n,e,2,t,e,P,n,e,a,t,a,n,a,o,a,t,e,v,=,d,t,d,t,切向加速度,R,v,n,e,2,a,=,n,法向加速度,a,v,=,d,t,d,t,R,v,2,a,=,n,a,t,a,n,+,=,返回,结束,第,1,页,/,共,20,页,t,e,P,n,e,a,t,a,n,a,o,2,a,=,a,t,a,n,+,2,v,=,d,t,d,R,v,2,2,2,+,a,=,t,a,n,arc tg,e,n,a,的夹角,与,a,=,n,a,t,q,arc tg,q,v,a,的夹角,与,t,e,a,t,a,n,a,o,q,v,n,e,或者用加速度与速度,方向的夹角来表示,第,2,页,/,共,20,页,讨论,:,a,+,t,e,v,=,d,t,d,R,v,n,e,2,a,t,a,n,+,=,v,方向的变化。,速度,v,大小的变化。,速度,法向加速度,a,n,R,v,n,e,2,=,的产生是,由于,物体在匀速率圆周运动中速度大小不变，,a,t,t,e,v,=,d,t,d,切向加速度,的产生是,由于,1.,R,v,2,只有速度方向的改变，所以加速度为,第,3,页,/,共,20,页,t,a,与,方向相反,v,a,a,n,t,a,v,a,与,成钝角,v,t,a,与,方向相同,v,a,与,成锐角,v,t,d,d,0,质点减速,v,a,a,n,t,a,v,a,并不指向圆心。,2,.,一般加速度,返回,第,4,页,/,共,20,页,近日点,加速区域,90,0,远日点,v,太阳,a,a,a,a,a,a,v,v,v,v,v,v,v,地球,太阳,a,a,返回,结束,第,5,页,/,共,20,页,a,d,d,t,=,t,v,3.,对于,任意平面曲线运动,曲率半径,a,2,n,=,v,o,v,t,a,n,a,y,y,2,3,=,(,),1,+,返回,结束,第,6,页,/,共,20,页,o,x,1.,角位置，角位移,角位置,角位移,2.,角速度,=,lim,t,0,t,=,d,d,t,(rad.s,-1,),=,t,二、圆运动的角量表示,A,.,t,B,.,t,+,t,平均角速度,瞬时角速度,返回,结束,第,7,页,/,共,20,页,lim,t,t,=,0,3.,角加速度,=,d,d,t,=,d,d,t,2,2,=,t,平均角加速度,瞬时角加速度,(rad.s,-2,),单位：,返回,结束,第,8,页,/,共,20,页,匀变速圆周运动的运动方程,x,v,t,0,=,+,a,0,t,t,0,=,+,+,1,2,2,匀速圆周运动的运动方程,0,t,0,=,+,0,=,2,2,2,0,(,),+,返回,结束,第,9,页,/,共,20,页,R,=,s,4.,线量和角量的关系,t,t,t,t,R,0,0,=,s,lim,lim,R,=,v,R,s,R,=,R,=,v,=,v,R,a,t,=,R,t,t,t,=,lim,lim,0,v,R,t,0,t,=,R,d,d,返回,结束,第,10,页,/,共,20,页,a,2,=,v,n,R,2,2,=,R,R,R,a,2,=,n,2,=,v,R,R,2,=,返回,结束,第,11,页,/,共,20,页,例,1,一质点作圆周运动，其路程与时间,的关系为,s,=,v,0,t,-,b t,2,/2,v,0,和,b,都是正的常,数。,(1),求质点在,t,时刻的速度;,(2),t,为何值时，质点的切向加速度和法,向加速度的大小相等。,返回,结束,第,12,页,/,共,20,页,a,=,n,v,R,2,(,),=,b,0,v,t,2,R,=,+,a,t,a,n,2,2,a,(,),=,+,(,),b,0,v,t,2,R,2,b,2,解：,(1),s,v,d,=,t,d,1,2,b,2,0,(,),d,=,t,d,v,t,t,=,b,0,v,t,a,=,t,v,d,t,d,(,),d,=,t,d,b,0,v,t,=,b,arc tg,(,),b,0,v,t,2,b,R,=,=,arc tg,a,t,a,n,a,t,a,n,a,v,返回,结束,第,13,页,/,共,20,页,(,),=,b,b,0,v,t,2,R,(2),由前面得到,：,a,t,=,b,a,=,t,a,n,根据题意,得到：,a,=,n,(,),b,0,v,t,2,R,解得：,返回,结束,(,),=,b,R,b,0,v,t,第,14,页,/,共,20,页,例,3,一质点作圆周运动，轨道半径为,R,，,其运动方程为：,=,ct,-,b t,2,c,和,b,都是正,的常数。,试求：质点在,t,时刻的切向加速度和法,向加速度。,2,t,c,b,=,q,d,=,d,t,w,d,=,d,t,=,2,b,R,a,=,t,2,R,a,=,n,w,R,2,(,),=,2,t,c,b,=,2,R,b,解：,返回,结束,第,15,页,/,共,20,页,返回,结束,圆周运动及其描述,一、切向加速度和法向加速度,a,+,t,e,v,=,d,t,d,R,v,n,e,2,a,t,e,v,=,d,t,d,t,切向加速度,R,v,n,e,2,a,=,n,法向加速度,a,v,=,d,t,d,t,R,v,2,a,=,n,a,t,a,n,+,=,t,e,P,n,e,a,t,a,n,a,o,第,16,页,/,共,20,页,返回,结束,t,e,P,n,e,a,t,a,n,a,o,2,a,=,a,t,a,n,+,2,v,=,d,t,d,R,v,2,2,2,+,a,=,t,a,n,arc tg,e,n,a,的夹角,与,o,v,t,a,n,a,3.,对于,任意平面曲线运动,a,d,d,t,=,t,v,曲率半径,a,2,n,=,v,y,y,2,3,=,(,),1,+,第,17,页,/,共,20,页,o,x,1.,角位置，角位移,角位置,角位移,2.,角速度,=,lim,t,0,t,=,d,d,t,(rad.s,-1,),=,t,二、圆运动的角量表示,A,.,t,B,.,t,+,t,平均角速度,瞬时角速度,返回,结束,第,18,页,/,共,20,页,lim,t,t,=,0,3.,角加速度,=,d,d,t,=,d,d,t,2,2,=,t,平均角加速度,瞬时角加速度,返回,结束,4.,线量和角量的关系,R,=,v,a,t,=,R,R,a,2,=,n,2,=,v,R,R,=,s,第,19,页,/,共,20,页,返回,结束,作业,1-8,，,1-9.,第,20,页,/,共,20,页,
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