What Is The Difference Between Frequency And Angular Frequency? (In-Depth)

If you’re a physics student, one thing that might confuse you a lot is the difference between frequency and angular frequency. Let’s unveil the difference between the two.

Frequency refers to the number of cycles that are completed every second, while angular frequency measures the angles or radians completed each second. 

Another major difference is that frequency is measured in hertz (Hz), while angular frequency is measured in radians/second. 

Without frequency, there would be no music, colors of light, radio, or x-rays.

If you’re interested in learning these concepts with the help of real-life examples, stick around and keep on reading.

Understanding Frequency: What It Means?

The frequency of an event is the number of times it occurs within a specified period.

A time period can be expressed in seconds, hours, days, or years. Hertz (Hz) is the unit of measure for frequency; it stands for cycles per second. 

For instance, if an object completes one circle in a second, its frequency would be 1 hertz, while the object completing two circles in a second will have a 2 Hz frequency. 

Example

Let’s have a look at the example of the clock speed of RAM to better understand the concept of frequency. 

It is the clock cycle speed that determines the CPU’s performance. CPU performance improves as the clock cycle speed increases. 

The number of clock cycles per second in the processor works on the concept of frequency. The speed of cycles per second can be measured in three different units: hertz, megahertz, and gigahertz. 

1MHz=1000000 Hz

1GHz=1000 MHz

Formula 

f=1/T 

What is Angular Frequency?

We have already established that frequency is the “number of times” a certain task is being timed in a given period of time. Angular frequency is the “number of angles” (radians) covered per unit of time (seconds).

Example

Consider a ball attached to the fixed point using a string. The ball, when moved, can move in a 360° circle. The number of radians the ball will cover in one second would be considered its angular frequency. And it’ll be measured in radians (another name for degrees) covered per unit of time.

Formula

The formula for angular frequency is:

ω=2π/T

What is Statistical Frequency? 

Since we are discussing frequencies, another important concept is statistical frequency. In statistics, frequency is defined as the number of times a value repeats in a sampling distribution. 

Example

Here’s an example: 

1, 2, 2, 2, 7, 5, 9, 9, 0, 0, 1, 5

• In the above table, I created 4 columns.
• The first column consists of serial numbers.
• The second column is named “X” containing all the values. 
• In the third column, I wrote the number of times a value has been repeated. As you can see, the value “zero” is repeated twice, therefore two is a frequency of 0. 
• You’ll see that the total frequency is equivalent to the number of values in the randomly distributed data. 
• The fourth and last column contains cumulative frequency. I wrote the first frequency value as it is. Then I kept adding the next value till the last value. 

Frequency vs. Angular Frequency

Frequency and angular frequency are terms that describe the rate of motion. The former is measured in cycles per second, while the latter is measured in radians per unit of time.

• When used in the same context, they are often used interchangeably. For instance, a merry-go-round rotates once per minute, while the moon moves once in 28 days.
• Angular frequency is a measurement of the angular displacement of a particle in a given time. It describes the angular position of a particle moving in a circular path.
• The angular frequency unit is radian/second, and the symbol for the angular frequency is omega (ω).
• Both terms describe motion, but the angular frequency is more commonly used for scientific purposes.
• Frequency is an umbrella term whereas angular frequency is a type or frequency like many other frequencies we study in science.

Difference Between Frequency and Angular Frequency: A Comparison

In physics, frequency is a measurement of the rate of vibrations or oscillations. The frequency is equal to the vibration frequency, creating the wave. For instance, a rope that is moved faster generates a higher frequency than one that moves at a slower speed. Likewise, higher-frequency waves are more energetic than lower-frequency waves.

Here’s a video differentiating frequency and angular frequency.

Angular Frequency vs. Angular Velocity

Angular frequency and angular velocity are both terms used to describe motion. Angular velocity is the speed of motion at which objects change direction or accelerate. While the two terms are related, they are not always the same.

For example, the difference between angular frequency and angular velocity is not as significant as that between velocity and time. In the scientific world, angular frequency and angular velocity are related terms.

• They are used to describe a system’s motion; however, they are not the same thing.
• The angular frequency refers to the number of angles that an object makes at a specific time. The angular frequency is typically expressed in radians per second while the angular velocity is the number of degrees per second.
• Angular frequency is the rate of change of angular displacement over a time period. In simple terms, this means that any particle that moves through a system has an angular frequency. It is also called the time period of a wave. This period is measured in seconds.
• An angular frequency is proportional to the angular velocity. For a given period, a certain angular frequency equals one revolution per second.
• However, when the angular frequency is too high, angular velocity decreases. This is the reason why it is important to calculate the angular frequency of a system before using it in engineering calculations.

Conclusion

• Frequency measures cycles per second. In contrast, angular frequency measures radians per second.
• Frequency is in hertz (Hz). And angular frequency is in radians/second.
• Both are crucial in understanding wave motion and rotational dynamics.
• Frequency is about vibrations, while Angular frequency is about things turning around.
• Angular frequency is denoted by the omega (ω) symbol. And it is used in scientific contexts.
• They serve different purposes in physics and engineering.
• Frequency is a general term for motion. Whereas angular frequency is specific to rotational motion.
• Understanding this difference is essential in physics and engineering.

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