题目内容
(13分)如图所示,在同一竖直平面内有A、B两物体,A物体从a点起以角速度ω沿顺时针方向做半径为R的匀速圆周运动,同时B物体从圆心O处自由下落.若要A、B两物体在d点相遇,求角速度ω须满足的条件.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/201408250037086953859.jpg)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/201408250037086953859.jpg)
ω=
π
(其中n=0,1,2……)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003708711724.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003708727575.png)
A物体到达d点的时间
tA=
T=![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003708711724.png)
(其中n=0,1,2……)
B物体到达d点的时间tB=
,tA=tB,![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003708711724.png)
=
,
解得ω=
π
(其中n=0,1,2……).
tA=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003708711724.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003708711724.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003708758510.png)
B物体到达d点的时间tB=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003708727575.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003708711724.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003708758510.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003708727575.png)
解得ω=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003708711724.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003708727575.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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