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老寇说

老寇说

好记性不如烂笔头
老寇说
线速度、角速度、转速

文章分类:水处理  发布时间:2024-05-27

要理解线速度、角速度、转速的转换之前,必须先理解一个概念,弧度制
我们习惯了一个圆是360°的概念,但表示角度的方法有很多,比如角度对应的弧长/半径 这个数值和360°概念的角度数值分别可以一一对应,同样表示角度
弧度的定义为 角度对应的弧长/半径,我们现在用弧度来表示角度
1、90°角的弧度很明显对应的是 2*pi*r/4/r=pi/2,同理,180°对应的是pi
2、角速度指的是角度的变化(这里的角度用弧度表示),角速度我们用ω表示
3、转速即圆周运动单位时间内转了多少圈
4、线速度指的是角度对应的弧长在单位时间内的变化量(注意和弧度的区分)

假设上侧圆的转速为 n 转/s 则有:
a、圆旋转1圈的时间为1/n
b、角速度ω为 2*pi*r/r(一圈的弧长/半径)/(1/n)=2*pi*n,或者直接理解一圈对应弧度制角度为2*pi,角速度为2*pi*n,角度的弧度制肯定是pi的倍数
c、从定义即可知线速度v=角速度*r=ω*r
d、线速度v=2*pi*n*r,另外一种理解线速度的方式为:周长/(1/n)=周长*n=2*pi*r*n
有很多种方法推导,但都有一个前提,弧度制,仔细理解

5/27/2024 11:24:53 PM

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