# Confusion about angular speed and angular acceleration

• Arman777
In summary, the conversation discusses the differences between angular speed and angular velocity in the context of frequency and angular displacement. It is explained that while frequency is a counting measure, angular velocity is a vector quantity with both direction and magnitude. The conversation also touches on the use of units and the importance of converting between frequency and angular speed in circuit calculations.
Arman777
Gold Member
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

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

Arman777
So angular velocity and angular speed is same in 1D ?

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.

Arman777
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.

Arman777
I understand I guess thank you all

## 1. What is the difference between angular speed and angular acceleration?

Angular speed is a measure of how fast an object rotates around a fixed point, while angular acceleration is a measure of how quickly the angular speed changes over time.

## 2. How are angular speed and linear speed related?

Angular speed and linear speed are related through the radius of rotation. Linear speed is equal to the angular speed multiplied by the radius of rotation.

## 3. Can angular acceleration be negative?

Yes, angular acceleration can be negative. This indicates that the object is slowing down in its rotation or changing direction.

## 4. How is angular acceleration measured?

Angular acceleration is measured in units of radians per second squared (rad/s²). This is the change in angular speed over time.

## 5. What is the difference between tangential acceleration and angular acceleration?

Tangential acceleration is a measure of how the linear speed of an object changes over time, while angular acceleration is a measure of how the angular speed changes over time. Tangential acceleration is caused by a change in the magnitude of the linear velocity, while angular acceleration is caused by a change in the direction of the angular velocity.

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