The dimensional formula of Acceleration is

**[ M**^{0}** L**^{1}** T**^{-2}** ]**

where **[M]**, **[L],** and **[T]** are the fundamental quantities: **Mass**, **Length**, and **Time**.

From the above formula, we can derive the **dimensions of acceleration as (0, 1, -2)**.

## Derivation of Dimensional Formula of Acceleration

We can derive this formula using the definition of acceleration.

In physics, we can define acceleration as the rate of change in speed. So, mathematically, acceleration is given as

```
Acceleration = Speed / time
```

We know **Speed = distance / time**. Substituting the value of **Speed** in the above equation, we get

```
Acceleration = ( distance / time ) / time
Acceleration = distance / time
```^{2}
Acceleration = distance^{1} * time^{-2}

Dimensionally, we use

**[L]**for distance**[T]**for time

Now the formula becomes

```
Acceleration = [L
```^{1}] * [T^{-2}]

Since the formula doesn’t include the fundamental quantity **Mass**, we can use **[M ^{0}]**, which is equal to

**1**.

```
Acceleration = [M
```^{0}] * [L^{1}] * [T^{-2}]

Hence, the **dimensional equation of acceleration is a = [ M ^{0} L^{1} T^{-2} ]**.

## What is the dimensional formula of angular acceleration?

The dimensional formula of angular acceleration is

**[M**^{0}** L**^{0}** T**^{-2}**]**

where **[M]**, **[L],** and **[T]** are the fundamental quantities: **Mass**, **Length**, and **Time**.

**Derivation**

We can define angular acceleration as the rate of change of angular velocity. So, the formula becomes

```
Angular Acceleration (α) = Angular Velocity (ω) / time (t)
```

Also, we can define **Angular Velocity** as the rate of change of angle **θ**. Hence,

```
Angular Velocity (ω) = Angle (θ) / time (t)
```

Substituting the value of **ω** in the first equation, we get

```
Angular Acceleration (α) = (Angle / time) / time
α = Angle / time
```^{2}
α = Angle * time^{-2}

In physics, **Angle** (θ) is a dimensionless quantity, and we use **[T]** to represent **Time**. Hence, the equation becomes

```
α = [T
```^{-2}]

Since the formula doesn’t include the fundamental quantities **Mass** and **Length**, we can use **[M ^{0}] * [L^{0}]**, which is equal to

**1**.

```
Angular Acceleration = [M
```^{0}] * [L^{0}] * [T^{-2}]

Hence, the **dimensional equation of angular acceleration is α = [M ^{0} L^{0} T^{-2}]**.

### 2. What is the dimensional formula of acceleration due to gravity?

The dimensional formula of acceleration due to gravity is

**[ M**^{0}** L**^{1}** T**^{-2}** ]**

where **[M]**, **[L],** and **[T]** are the fundamental quantities: **Mass**, **Length**, and **Time**.

**Derivation**

In physics, we can define acceleration due to gravity as the acceleration of a free-falling body due to gravitational force.

We know the formula of Force,

```
Force = mass * acceleration due to gravity (g)
g = Force / mass
```

The dimensional formula of Force is **[ M ^{1} L^{1} T^{-2} ]**, and we represent

**mass**with

**[M]**. Hence, the formula becomes

```
g = [ M
```^{1} L^{1} T^{-2} ] / [M^{1}]
Acceleration due to gravity = [ M^{0} L^{1} T^{-2} ]

Hence, the **dimensional equation of acceleration due to gravity is g = [ M**^{0}** L**^{1}** T**^{-2}** ]**.

**Related Articles**