小班讲义高一物理第12讲圆周运动

1、龙 文 教 育精品小班课程辅导讲义讲义编号 2013秋季 辅导科目： 物理 年级： 高一课 题第12讲：圆周运动教学目标教学重点、难点教学内容1.定义： 质点沿圆周运动，如果在相等时间里通过的圆弧的长度相等，这种运动叫做匀速圆周运动.基本知识点：匀速圆周运动（性质：非匀变速曲线运动）是瞬时加速度、速度矢量方向不断改变的变速运动.（“匀速”指速率不变） 匀速圆周运动的快慢，可以用线速度来描述.（v为线速度大小，s为弧长）线速 度的方向在圆周该点的切线方向（不断变化）. 匀速圆周运动的快慢，可以用角速度来描述.（国际制单位：弧度每秒，符号是 （rad/s）（为角速度符号，为半径转过角度） 匀速圆周

2、运动的快慢，可以用周期来描述.（匀速圆周运动是一种周期性的运动） 符号：t（，为时间，为圈数）. 周期长说明物体运动的慢，周期短说明物体运动的快. 周期的倒数是频率，符号f.频率高说明物体运动的快，频率低说明物体运动的慢. 匀速圆周运动的快慢，可以用转速来描述.转速是指每秒转过的圈数， 用符号n表示.单位转每秒，符号r/s（n换成这个单位才等于f）. 固定在同一根转轴上的转动物体，其角速度大小、周期、转速相等（共轴转动）； 用皮带传动、铰链转动、齿轮咬合都满足边缘线速度大小相等. 匀速圆周运动是角速度、周期、转速不变的运动，物体满足做匀速圆周运动的条 件：有向心力、初速度不为零.向心力只改变线

3、速度方向，不改变大小（向心加速度的作用：描述线速度方向变化快慢）.2. 向心力定义：使物体速度发生变化的合外力.基本知识点：向心力的方向总是指向圆心（与线速度方向垂直），方向时刻在变化，是一个变力. 向心力是根据力的作用的效果命名的.它可以是重力、弹力、摩擦力等各种性质 的力，也可以是某个力的分力. 匀速圆周运动的向心力大小f向心 f向心=3. 向心加速度方向总是指向圆心. 基本知识点：向心力产生向心加速度只是描述线速度方向变化的快慢. 向心加速度的方向总是指向圆心，但时刻在变化，是一个变加速度. 作曲线运动的物体的加速度与速度方向不在一条直线上. （速度方向是轨迹的切线方向，加速度方向是合外

4、力方向）4. 匀速圆周运动实例分析： 火车转弯情况：外轨略高于内轨，使得所受重力和支持力的合力提供向心力，以减少 火车轮缘对外轨的压力. 当火车行使速率v等于v规定时，f合=f向心，内、外轨道对轮缘都没有侧压力. 当火车行使速率v大于v规定时，f合f向心，外轨道对轮缘都有侧压力. 当火车行使速率v小于v规定时，f合f向心，内轨道对轮缘都有侧压力. 没有支承物的物体（如水流星）在竖直平面内做圆周运动过最高点情况： 当，即，水恰能过最高点不洒出，这就是水能过最高点的临界 条件； 当，即，水不能过最高点而洒出； 当，即，水能过最高点不洒出，这时水的重力和杯对水的压力 提供向心力. 有支承物的物体（如

5、汽车过拱桥）在竖直平面内做圆周运动过最高点情况： 当v=0时，支承物对物体的支持力等于mg ，这就是物体能过最高点的临界条件； 当时，支承物对物体产生支持力，且支持力随v的减小 而增大，范围（0mg） 当时，支承物对物体既没有拉力，也没有支持力. 当时，支承物对物体产生拉力，且拉力随v的增大而增大. （如果支承物对物体无拉力，物体将脱离支承物）5竖直平面内的圆周运动任意动力学问题处理方法：正交分解法将牛顿第二定律fma用于变速圆周运动，f是物体所受的外力，不一定是向心力，a是物体运动的加速度，不一定是向心加速度采用正交分解法，沿法向（正方向沿着半径指向圆心），切向分解法向合力为向心力，其作用是

6、改变速度的方向，法向加速度即为向心加速度an，其大小反映速度方向变化的快慢切向合力使物体产生切向加速度a，其作用是改变速度的大小 6. 作匀速圆周运动的物体.在合外力突然消失或者不足以匀速圆周运动所需的向心力的情 况下，就做离心运动.反之，为向心运动.例1在用高级沥青铺设的高速公路上，汽车的设计时速是108km/h汽车在这种路面上行驶时，它的轮胎与地面的最大静摩擦力等于车重的0.6倍如果汽车在这种高速路的水平弯道上拐弯，假设弯道的路面是水平的，其弯道的最小半径是多少？如果高速路上设计了圆弧拱桥做立交桥，要使汽车能够安全通过圆弧拱桥，这个圆弧拱桥的半径至少是多少？例2如图所示，支架质量为m，放在

7、水平地面上，转轴o处用长为l的细绳悬挂一质量为m的小球，问：（1）若小球从悬线呈水平位置释放后，当它运动到最低点时地面对支架的支持力为多大？（2）若小球在竖直平面内摆到最高点时，支架恰好对地面无压力，则小球在最高点时的速度为多大？例3轻杆oa长0.5m，在a端固定一小球，小球质量m为0.5kg，以o点为轴使小球在竖直平面内做圆周运动，当小球到达最高点时，小球的速度大小为v0.4m/s，求在此位置时杆对小球的作用力（g取10m/s2）例4一个内壁光滑的环形细圆管，位于竖直平面内，环的半径为r（比细管的半径大得多），圆管中有两个直径与细管内径相同的小球（可视为质点）a球的质量为m1，b球的质量为m

8、2它们沿环形圆管顺时针运动，经过最低点时的速度都为v0设a球运动到最低点时，b球恰好运动到最高点，若要此时两球作用于圆管的合力为零，求m1，m2，r与v0应满足关系例5如图所示，光滑水平面上，小球m在拉力f作用下作匀速圆周运动。若小球运动到p点时，拉力f发生变化，关于小球运动情况的说法正确的是( )a.若拉力突然消失，小球将沿轨迹pa做离心运动 b.若拉力突然变小，小球将沿轨迹pa做离心运动 c.若拉力突然变大，小球将沿轨迹pb做离心运动 d.若拉力突然变小，小球将沿轨迹pc 运动例6如图所示，倾斜放置的圆盘绕着中轴匀速转动，圆盘的倾角为37，在距转动中心0.1m处放一小木块，小木块跟随圆盘一

9、起转动，小木块与圆盘的动摩擦因数为0.8 ，木块与圆盘的最大静摩擦力与相同条件下的滑动摩擦力相同。若要保持木块不相对圆盘滑动，圆盘转动的角速度最大值约为( )a.8rad/s b.2rad/s c. d. 例7如图所示为电动打夯机的示意图，在电动机的转动轴o上装一个偏心轮，偏心轮的质量为m，其重心离轴心的距离为r，除偏心轮之外，整个装置其余部分的质量为 m 。当电动机匀速转动时，打夯机的底座在地面上跳动而将地面打实夯紧。分析并回答：( 1 ）为了使底座刚好跳离地面，偏心轮的最小角速度，应是多少？ ( 2 ）如果偏心轮始终以这个角速度0转动，底座对地面压力的最大值为多少？例8半径为r的光滑半圆球

10、固定在水平面上，如图所示，顶部有一小物块若使小物块无速度向右滑下，则物块是否能沿着球面一直滑到m点？如若不能，物块在何处与半圆球分离例9如图所示轻杆长 lm ，其两端各连接质量为 1 kg 的小球，杆可绕距 b 端0.2m 处的轴 o 在竖直平面内自由转动，轻杆由水平从静止转至竖直方向， a 球在最低点时的速度为 4m / s (g取l0m/s2）求： ( 1 ) a 小球此时对杆的作用力大小及方向( 2 ) b 小球此时对杆的作用力大小及方向。例10拍苍蝇与物理学中的圆周运动有关。市场出售的蝇拍，拍把长约30cm，拍头是长12cm、宽10cm的长方形。这种拍的使用效果往往不好，当拍头打向苍蝇

11、，尚未打到，苍蝇就飞走了。有人将拍把增长到60cm，结果击中苍蝇的几率大大提高。你能解释其原因吗？ 第 12 次课后作业学生姓名： 1汽车通过拱桥顶点的速度为10m/s时，车对桥的压力为车重的3/4如果使汽车行驶至桥顶时对桥恰无压力，则汽车的速度为（）a15 m/s b20 m/s c25 m/s d30 m/s2如图所示，一个质量为m的小球，用长为l的悬线固定于o点，在o点正下方l/3处钉一铁钉p，把悬线拉到水平方向由静止释放后，当悬线碰到钉子的瞬间，下列判断正确的是（）a小球的速度突然增大b小球的向心加速度突然增大c小球的角速度突然增大d悬线的拉力突然增大3如图所示，长为l的轻杆，一端固定

12、一个小球，使轻杆与小球一起绕o点在竖直平面内做圆周运动，关于小球在最高点的速度v，下列说法中正确的是（）av的极小值为（gl）1/2bv由零逐渐增大时，向心力也逐渐增大c当v由（gl）1/2逐渐减小时，杆对小球的弹力逐渐增大d当v由（gl）1/2逐渐增大时，杆对小球的弹力逐渐增大4如图所示，细杆的一端与一小球相连，可绕过o点的水平轴自转动现给小球一初速度，使它做圆周运动，图中a、b分别表示小球轨道的最低点和最高点，则杆对小球的作用力可能是（ ）aa处为拉力，b处为拉力 ba处为拉力，b处为推力ca处为推力，b处为拉力 da处为推力，b处为推力5 如图在粗糙水平木板上放一物块，沿图所示的逆时针方

13、向做匀速圆周运动，圆半径为 r , 速率v，ab为水平直径，cd为竖直直径。设运动中木板始终保持水平，物块相对于木板静止，则下列判断中正确的是（ ) a.物块始终受四个力作用 b.只有在a、b、c、d四点，物块受到的合外力才指向圆心c.从a运动到b，物块处于超重状态 d.从b运动到a，物块处于超重状态5如图所示，在电机距轴o为r处固定一质量为m的铁块电机启动后，铁块以角度绕o匀速转动则电机对地面的最大压力和最小压力之差为6一架飞机，在竖直平面内沿半径为500m的“8”字形轨道做特技飞行，如图所示，已知飞行员的质量为60kg，飞机的飞行速度为360km/h,求在最高点或最低点a、b、c、d四个位

14、置上，座椅或保险带对飞行员的作用力7质量为0.5kg的小杯里盛有1kg的水，用绳子系住小杯在竖直平面内做“水流星”表演，转动半径为1m，小杯通过最高点的速度为4m/s，g取10m/s2，求：（1）在最高点时，绳的拉力？（2）在最高点时水对小杯底的压力？（3）为使小杯经过最高点时水不流出，在最高点时最小速率是多少?8一质量为m的金属小球用l长的细线拴住，固定在一点o，然后将线拉至水平，在悬点o的正下方某处p钉一光滑钉子，如图所示，为使悬线从水平释放碰钉后小球仍做圆周运动，则op的最小距离是多少？（g10m/s2）9如图所示，半径为r、内径很小的光滑半圆管竖直放置，两个质量均为m的小球a、b，以不

15、同的速度进入管内，a通过最高点c时，对管壁上部的压力为3mg，b通过最高点时，对管壁下部的压力为0.75mg，则a、b两球落地点的距离为多大?10左下图所示为一根竖直悬挂的不可伸长的轻绳，下端拴一小物块a，上端固定在c点且与一能测量拉力的测力传感器相连已知有一质量为m0的子弹b沿水平方向以速度v0射入a内（未穿透），接着两者一起绕c点在竖直面内做圆周运动各种阻力都可忽略的条件下测力传感器测得绳的拉力f随时间t的变化关系如右下图所示已知子弹射入的时间极短，且右下图中t0为a、b开始以相同速度运动根据力学规律和题中（包括图）提供的信息，对反映悬挂系统本身性质的物理量（例如a的质量）及a、b一起运动

16、过程中的守恒量，你能求得哪些定量的结果？ winger tuivasa-sheck, who scored two tries in the kiwis 20-18 semi-final win over england, has been passed fit after a lower-leg injury, while slater has been named at full-back but is still recovering from a knee injury aggravated against usa.both sides boast 100% records headi

17、ng into the encounter but australia have not conceded a try since josh charnleys effort in their first pool match against england on the opening day.aussie winger jarryd hayne is the competitions top try scorer with nine, closely followed by tuivasa-sheck with eight.but it is recently named rugby le

18、ague international federation player of the year sonny bill williams who has attracted the most interest in the tournament so far.the kiwi - with a tournament high 17 offloads - has the chance of becoming the first player to win the world cup in both rugby league and rugby union after triumphing wit

19、h the all blacks in 2011.id give every award back in a heartbeat just to get across the line this weekend, said williams.the (lack of) air up there watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and

20、 will attend citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its about how he felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings a

21、gainst cskafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs governing body, has also ordered an immediate investigation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian s

22、ide added: we found no racist insults from fans of cska. baumgartner the disappointing news: mission aborted.the supersonic descent could happen as early as sunda.the weather plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, wit

23、h no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher t

24、han the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly

25、 step out onto something resembling an olympic diving platform.they blew it in 2008 when they got caught cold in the final and they will not make the same mistake against the kiwis in manchester.five years ago they cruised through to the final and so far history has repeated itself here - the last t

26、ry they conceded was scored by englands josh charnley in the opening game of the tournament.that could be classed as a weakness, a team under-cooked - but i have been impressed by the kangaroos focus in their games since then.they have been concentrating on the sort of stuff that wins you tough, eve

27、n contests - strong defence, especially on their own goal-line, completing sets and a good kick-chase. theyve been great at all the unglamorous stuff that often goes unnoticed in the stands but not by your team-mates.it is as though their entire tournament has been preparation for the final.in johna

28、than thurston, cooper cronk, cameron smith and either billy slater or greg inglis at full-back they have a spine that is unmatched in rugby league. they have played in so many high-pressure games - a priceless asset going into saturday.the kiwis are a lot less experienced but winning a dramatic matc

29、h like their semi-final against england will do wonders for their confidence.they defeated australia in the four nations final in 2010 and the last world cup, and know they can rise to the big occasion.winger tuivasa-sheck, who scored two tries in the kiwis 20-18 semi-final win over england, has bee

30、n passed fit after a lower-leg injury, while slater has been named at full-back but is still recovering from a knee injury aggravated against usa.both sides boast 100% records heading into the encounter but australia have not conceded a try since josh charnleys effort in their first pool match again

31、st england on the opening day.aussie winger jarryd hayne is the competitions top try scorer with nine, closely followed by tuivasa-sheck with eight.but it is recently named rugby league international federation player of the year sonny bill williams who has attracted the most interest in the tournam

32、ent so far.the kiwi - with a tournament high 17 offloads - has the chance of becoming the first player to win the world cup in both rugby league and rugby union after triumphing with the all blacks in 2011.id give every award back in a heartbeat just to get across the line this weekend, said william

33、s.the (lack of) air up there watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i have asked to

34、 meet yaya toure, he told bbc sport.for me its about how he felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs g

35、overning body, has also ordered an immediate investigation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska. baumgartner the disappointing news: mission aborted.the supers

36、onic descent could happen as early as sunda.the weather plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower

37、 level of the atmosphere (the troposphere) where our day-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses

38、the boundary layer (called the tropopause),e can expect a lot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto something resembling an olympic diving platform.they blew it in 2008 when they got caught cold in the final and they will not make