Change in Momentum Calculator

The change in momentum calculator evaluates the change in momentum of an object by-product of mass and change in velocity.

How to Find Change in Momentum?

The change in momentum is the difference between the initial and final momentum of an object. The momentum of an object is changed due to the velocity of an object. The formula for change in momentum is given by:  

Δp = m * v

The momentum change formula can be elaborated in more detail as below:

Δp = p₂ – p₁ = m_2 * v₂ – m_2 * v₁ = m * Δv

Here the Δp represents the change in momentum over a particular period of time. So to calculate change in momentum, you need to subtract the “p₂” final momentum from the “p₁”initial momentum caused by change of velocity.  The final momentum calculator is going to identify the change in momentum of an object with respect to it momentum shift.

What is Impulse?

The change in momentum is known to be the impulse and it is represented as the “J”. The formula for calculating change in momentum or impulse is given by:

J = F * t

J = Δp

The units of impulse or momentum are  “Ns” or  kg*m/s If you are finding the impulse or the change of momentum then check the answers using the impulse and momentum calculator. Both the terms are same in their meaning and purpose in the field of physics.

Practical Example:

Let’s calculate change in momentum of an object of mass 100 Kg and uniformly accelerated from an initial velocity of 5 m s^−1 to 8 m s^−1 in a period of 6 seconds.

Given:

Initial velocity = u = 5 m/s.

Final velocity = v = 8 m/s.

Mass = m = 100 kg.

Time = t = 6 s.

Solution:

The momentum change formula for the initial momentum is:

Initial momentum = m*u 

Then 

Initial momentum =p₁=m*u = 100 × 5 = 500 kg m s−1

The final momentum  =p₂ = m*v = 100 × 8 = 800 kg m s−1

Now by applying the formula for change in momentum

Δp = p₂ – p₁ = m * v₂ – m * v₁ = m * Δv

Δp = p₂ – p₁ =  (800)-(500)

Δp = 300  kg m s−1

The change in momentum is also known to be the impulse of a moving object and you can identify the momentary impulse of an object by the impulse and momentum calculator.

Now to find the force acting on the object, we do the following calculation:

F = mv – mu / t

F = m (v-u) / t

F = 800 – 500

F = 300 / 6

F = 50 N

The following results are given below:

Initial momentum =p₁= mu = 500 kg m s^−1.

Final momentum =p₂= mv = 800 kg m s^−1.

The magnitude of the force =F = 50 N.

The total momentum calculator finds momentum and the applied force on the object.

How to Find Momentum with Force and Time?

According to Newton’s second law of motion, force is equal to the product of the mass and acceleration. 

Now:

F = ma 

Here”

Enter the values of (ΔM) and Force (F) in the change in momentum calculator to identify the momentum at any specific moment.

Acceleration is the change in the velocity with respect to the time

Acceleration = a = Δv/t

Then 

Force  = ma = m * Δv/t

Since:

Δp =m * Δv

Then  

Force = Δp /t  F = Δp /t 

Now by interchanging the values:

Δp = Force x  t 

Δp = F x  t 

The change of the momentum and the applied force are actually directly proportional to each other. Even our change in momentum calculator makes your momentum-changing calculations possible by considering parameters defined in Newton's second law of motion. 

Working of Change in Momentum Calculator:

Let’s have a look at the working of the total momentum calculator:

Input:

• Select the desired measurements from the list
• Enter the mass, initial velocity, and final velocity 
• Tap the calculate button

Output:

• Initial momentum 
• Final momentum 
• Change in momentum

References:

From the source of Wikipedia: How to solve for momentum, How to calculate change in momentum? From the source of the openstax.org: Momentum change formula, How to find the change in momentum?