角频率

Multi tool use
在物理学(特别是力学和电子工程)中,角频率ω有时也叫做角速率、角速度标量,是对旋转快慢的度量,它是角速度向量ω→{displaystyle {vec {omega }}}
的模。角频率的国际单位是弧度每秒。由于弧度是无量纲的,所以角频率的量纲为T −1。
因为旋转一周的弧度是2π,所以
- ω=2πT=2πf=v/r=dsdt⋅1r=dθdt{displaystyle omega ={frac {2pi }{T}}=2pi f=v/r={frac {ds}{dt}}cdot {frac {1}{r}}={frac {dtheta }{dt}}}

其中
ω是角频率(单位为弧度每秒)
T是周期(单位为秒)
f是频率(单位为赫兹)
v是绕轴旋转的线速度(单位为米每秒)
r是旋转的半径(单位为米)
角频率在数值上是频率的2π倍。很多情况下,使用角频率而不是频率作为变量可以避免出现额外的π,从而简化公式。物理学中包含周期运动的领域通常都使用角频率作为记号,例如量子力学和电动力学。
例如:
- a=−ω2x{displaystyle a=-omega ^{2}x}

如果用频率作为变量,这一等式要写作:
- a=−4π2f2x{displaystyle a=-4pi ^{2}f^{2}x}

與角速度的关系
角頻率為角速度量值的大小,其單位為rad/sec。
而頻率的單位是1/sec。
参见
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