角速度是物体在一段时间内的角位置变化率的量度。用于角速度的符号通常是小写的希腊符号omega，ω。角速度以每个时间的弧度或每次的度数（通常是物理学中的弧度）为单位表示，相对简单的转换允许科学家或学生使用每秒弧度或每分钟度数或在给定的旋转情况下需要的任何配置，无论是大型摩天轮还是溜溜球。 （有关执行此类转换的一些提示，请参阅我们关于尺寸分析的文章。）细心的读者会注意到与从对象的已知起点和终点位置计算标准平均速度的方式相似。以同样的方式，您可以继续在上方进行越来越小的Δt测量，其越来越接近瞬时角速度。瞬时角速度ω被确定为该值的数学极限，其可以使用微积分表示为：瞬时角速度：ω=极限，因为Δt接近Δθ/Δt=dθ/ dt的0 那些熟悉微积分的人会发现这些数学重构的结果是瞬时角速度ω是θ（角位置）相对于t（时间）的导数…这正是我们对角度的初始定义速度是，所以一切都按预期进行。计算角速度需要理解物体的旋转运动θ。旋转物体的平均角速度可以通过知道特定时间t1的初始角度位置θ1和特定时间t2的最终角度位置θ2来计算。结果是角速度的总变化除以总的时间变化产生平均角速度
Angular velocity is a measurement of the rate of change of angular position of an object over a period of time. The symbol used for angular velocity is usually a lower case Greek symbol omega, ω. Angular velocity is represented in units of radians per time or degrees per time (usually radians in physics), with relatively straightforward conversions allowing the scientist or student to use radians per second or degrees per minute or whatever configuration is needed in a given rotational situation, whether it be a large ferris wheel or a yo-yo. (See our article on dimensional analysis for some tips on performing this sort of conversion.) The attentive reader will notice a similarity to the way you can calculate standard average velocity from the known starting and ending position of an object. In the same way, you can continue to take smaller and smaller Δt measurements above, which gets closer and closer to the instantaneous angular velocity. The instantaneous angular velocity ω is determined as the mathematical limit of this value, which can be expressed using calculus as: Instantaneous Angular Velocity: ω = Limit as Δ t approaches 0 of Δ θ / Δ t = dθ / dt
Those familiar with calculus will see that the result of these mathematical reformulations is that the instantaneous angular velocity, ω, is the derivative of θ (angular position) with respect to t (time) … which is precisely what our initial definition of angular velocity was, so everything works out as expected. Calculating angular velocity requires understanding the rotational motion of an object, θ. The average angular velocity of a rotating object can be calculated by knowing the initial angular position, θ1, at a certain time t1, and a final angular position, θ2, at a certain time t2. The result is that the total change in angular velocity divided by the total change in time yields the average angular velocity