Dimensions of Angular Speed

Dimensional Formula of Angular Speed is M⁰L⁰T^-1. Dimensional formulas are very relevant in the field of physics because they give some ideas about how each dimension depends on while deriving a specific equation. Here in this article, we will be discussing the definition of Angular speed and the Dimensional Formula of Angular Speed along with its derivation.

Dimensional Formula is the formula which represents a physical quantity in the terms of fundamental physical quantities.

Angular Speed

Angular speed can be defined as the rate of change of angular displacement of a rotating body. It can be calculated in terms of the number or rotations or revolutions made by a body to the time it took. And it can be denoted as ‘ω’. It’s SI unit is rads per second. The formula for angular speed ω with angular displacement θ at time t is given by:

ω = θ / t

where,

• ω is angular speed
• θ is angular displacement
• t is time

What is Dimensional Formula of Angular Speed?

Dimensional Formula of Angular speed is M⁰L⁰T^-1

Where

• M denotes mass,
• L denotes length
• T denotes Time.

So we can say that:

• Mass has no effect in Angular speed.
• Length has no effect in Angular speed.
• Time is inversely proportional to Angular speed.

Angular Speed Equations

Consider the below image:

ω = θ/t —-(1)

θ- Angle made

t-time

ω = v/r —-(2)

v-Linear speed

r- Radius of circular path

Derivation for Dimensional Formula of Angular Speed

We know that angular speed is given by:

ω = 2π / Time

ω = 2π × [Time]^-1 ——(1)

In the above formula, 2π is dimensionless and the dimensional formula for time is [T].

Putting in equation (1)

So, the dimensional formula for the angular speed = [M⁰L⁰T^-1]

Dimensional formula of Angular speed= [M⁰L⁰T^-1 ]

Advantages of Dimensional Formula

Some advantages of representing physical quantity through its dimensional formula is:

• It is used to derive the relation between physical quantities.
• It can be used to change from one unit to another unit.
• It can be used to check the consistency of dimensional equation.

Limitations of Dimensional Formula

The main limitation of the dimensional formula is that it cannot be used to verify whether the formula for the given quantity is correct or not.

Read More

• Dimensional Formula
• Speed and Velocity

FAQs on Dimensional Formula of Angular Speed

1. What is the Dimensional Formula of Angular Speed?

Dimensional formula of Angular speed is M⁰L⁰T^-1

2. What are the Dimensions that are Proportional to the Angular Speed?

The angular speed is not proportional to any dimension.

3. Which could cause Decreasing the Value of Angular Speed?

The value of angular speed can decrease due to time.

4. What is the Unit of Angular Speed?

The unit of angular speed is revolutions per second OR rad/s.

5. How does Angular Speed relate to Frequency?

The angular speed is related to frequency as given below:

ω=2πf

where f is frequency

6. Can Angular Speed be Negative?

Yes, It can be. Positive angular speed denotes counterclockwise direction. Negative angular speed indicates clockwise direction.

7. Can Angular Speed be Zero?

Yes, it can be. It indicates that the object is at rest or there is not any angular displacement take place.

8. What is the Unit and Dimension of Angular Speed?

The unit of angular speed is revolutions per second OR rad/s and its dimension is [M⁰L⁰T^-1]

9. Is Dimensional Formula of Angular Velocity and Angular Speed Same?

Yes, the dimensional formula of Angular Velocity and Angular Speed are same and is given as [M⁰L⁰T^-1]