Currently, in the International System of Units (SI), reciprocal second (s⁻¹) and radian per second (rad s⁻¹) are the units of frequency ν and angular frequency ω, respectively. At the same time, these quantities are related in the SI by the simple mathematical relationship ω = 2πν. And here an evident conflict between this relation and the dimensions of the quantities included in it arises. When using the units in question, the two sides of this relation have different dimensions, which is not admissible in either physics or metrology. However, this situation has existed in metrology for many years. In 2019, the angular frequency with unit rad s⁻¹ was included in the SI brochure. This article analyzes the reasons that have led to this conflict and establishes the relationship between frequency, angular frequency and angular velocity. An example of a simple oscillatory system shows that ω and ν have the same dimension, inverse to the dimension of the time. Therefore, they are measured by the same unit s⁻¹. This does not coincide with the current definition of the unit of angular frequency in the SI, but fully corresponds to the laws of physics and removes the contradiction in the relation ω = 2πν. It is also shown that the angular frequency and angular velocity are independent quantities of different dimensions.

目前，在国际单位制（SI）中，倒数秒（s ^-1）和每秒弧度（rad s ^-1）分别是频率ν和角频率ω的单位。同时，这些量在 SI 中通过简单的数学关系ω = 2 πν 相关。在这里，这种关系与包含在其中的量的维度之间出现了明显的冲突。使用所讨论的单位时，这种关系的两侧具有不同的尺寸，这在物理学或计量学中都是不允许的。但是，这种情况在计量学中已经存在多年。2019年角频率单位为rad s ⁻¹已包含在 SI 手册中。本文分析了导致这种冲突的原因，并建立了频率、角频率和角速度之间的关系。一个简单振荡系统的例子表明ω和ν具有相同的量纲，与时间的量纲相反。因此，它们以相同的单位s ^-1来衡量。这与 SI 中角频率单位的当前定义不符，但完全符合物理定律并消除了关系ω = 2 πν中的矛盾。还表明角频率和角速度是不同量纲的独立量。