Dimensions of Angular Frequency
Angular frequency is a measure of how quickly an object is rotating or oscillating in a circular motion. It is denoted by the symbol ω and is measured in radians per second (rad s^-1).

Explanation of Dimensions
1. Angular Frequency:
- Angular frequency is a derived unit and is dimensionally equivalent to frequency, which is measured in Hz (hertz).
- The dimension of frequency is T^-1, where T represents time.
2. Radians:
- Radians are a unit of measurement for angles, and they are dimensionless.
- Since angular frequency is measured in radians per second, the dimensions of angular frequency are simply T^-1.
3. Length Dimensions:
- Angular frequency does not have dimensions of length because it is a measure of how quickly an object is rotating or oscillating, not a measure of distance or displacement.
- The dimensions of angular frequency are solely based on time.
In conclusion, the dimensions of angular frequency are T^-1, representing the inverse of time. It is important to distinguish between angular frequency and linear frequency, as they have different dimensions and physical interpretations.