Dimensional Formula of Linear and Angular Momentum

In this article, you will learn to calculate the dimensional formula of linear momentum and angular momentum.


Dimensional Formula of Linear Momentum

The dimensional formula of Linear Momentum is 

[ M1  L1  T-1 ]

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

From the above formula, the dimensions of momentum are (1, 1, -1).

We can derive this formula using the definition of linear momentum.


Derivation of Dimensional Formula of Linear Momentum

In physics, we can define momentum as the quantity of motion contained in a moving body. Mathematically, it is given as the product of mass and velocity.


  Momentum (P) = mass * velocity

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


  Momentum (P) = mass * (distance / time)

            P  = mass * distance * time-1

Dimensionally, we use

  • [M] to represent mass
  • [L] for distance
  • [T] to represent time

Now the formula becomes


  Linear Momentum = [M1] * [L1] * [T-1]

Hence, the dimensional equation of momentum is P = [ M1 L1 T-1 ].

Derivation of dimensional formula of momentum

Dimensional Formula of Angular Momentum

Similarly, the dimensional formula of angular momentum is 

[ M1  L2  T-1 ]

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

From the above formula, the dimensions of angular momentum are (1, 2, -1).

We can derive this formula using the formula of angular momentum.


Derivation of Dimensional Formula of Angular Momentum

In Physics, we can define angular momentum as a physical quantity possessed by a body moving around a point. Mathematically, it is given as the product of mass, velocity, and radius.


  Angular Momentum (J) = mass * velocity * radius

Angular Momentum (J) = mass * velocity * radius

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


  Angular Momentum = mass * (distance / time) * radius
  
                   = (mass * distance * radius) / time

                   = mass * distance * radius * time-1

Dimensionally, we use

  • [M] to represent mass
  • [L] for both distance and radius
  • [T] to represent time

Hence, the formula becomes


  Angular Momentum  = [M1] * [L1] * [L1] * [T-1]

                    = [M1] * [L2] * [T-1]

Hence, the dimensional equation of angular momentum is J = [ M1 L2 T-1 ].

Derivation of dimensional formula of angular momentum

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