# I Confusion about angular speed and angular acceleration

1. Feb 6, 2017

### Arman777

In my textbook.In some question gives me angular speed as ( )rev/s.I know that its the frequency (f).But some questions It says angular velocity and says rad/s.

Interesting thing happens when the textbook says in angular speed and I use f and then using w=2πf and then continue I get wrong answer but sometimes right answer.I am really confused

2. Feb 6, 2017

### BvU

There's good info to be googled, like here and here

3. Feb 6, 2017

### Arman777

So angular velocity and angular speed is same in 1D ?

4. Feb 6, 2017

### Svein

OK. By definition $\omega =\frac{d\phi}{dt}$ with dimension $\frac{rad}{s}=\frac{1}{s}$ (radian is dimensionless). The number of revolutions per second is a counting measure and since a count is dimensionless, it also has the dimension $\frac{1}{s}$.

In electronics we traditionally talk about frequency and measure it in Hz. Again, that is a counting measure - the number of wave maxima in a second. As such it is easy to measure using a counter or an oscilloscope. But once we need to do some circuit calculations, we must convert the frequency to angular speed.

5. Feb 6, 2017

### jack action

Frequency is the number of occurrences of a repeating event per unit time. (source)

So, in essence, frequency is the measure of something per unit time. It is often the measure of turns (or revolutions) per unit time because the best way to having something repeating itself is to go in a circle. Since one turn is also an angular displacement of $2\pi$ radians then, in such a case, the frequency can be related to an angular speed. But you cannot use the unit rad/s and call it a frequency, it must be turn/s absolutely (something that can be counted instead of measured). This is why we always do the transformation $\omega = 2\pi f$ instead of just doing a unit conversion.

Angular velocity is defined as the rate of change of angular displacement and is a vector quantity (source). A vector has a direction and a magnitude. Angular speed is the magnitude of that vector.

6. Feb 6, 2017

### Arman777

I understand I guess thank you all