题目内容
如图所示的皮带传动装置中,轮A和B同轴,A、B、C分别是三个轮边缘的质点,且RA=RC=2RB,若皮带不打滑,则A、B、C三点的角速度之比ωA:ωB:ωc = ,向心加速度之比aA : aB : aC = 。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241911452309831.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241911452309831.png)
2:2:1 4:2:1
试题分析:由于B轮和C轮是皮带传动,皮带传动的特点是两轮与皮带接触点的线速度的大小与皮带的线速度大小相同,故
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824191145558467.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824191145807543.png)
由于A轮和B轮共轴,故两轮角速度相同,即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824191146166508.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824191146478580.png)
由角速度和线速度的关系式
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824191146728476.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824191146962748.png)
所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824191147274617.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824191147539684.png)
又因为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824191147788673.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824191148054581.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824191148350733.png)
点评:解决传动类问题要分清是摩擦传动(包括皮带传动,链传动,齿轮传动,线速度大小相同)还是轴传动(角速度相同).
![](http://thumb2018.1010pic.com/images/loading.gif)
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