# Impulse and Momentum Calculator

Use the impulse and momentum calculator to analyze any given object in motion. There are different ways to calculate impulse. One way is to use the change in velocity of any given body. Another way is to use the time by which a force acts on any given body. The last way is to use the change of momentum. Let’s cover in detail using the calculator and performing the different calculations.

## How to use the momentum calculator?

Although this momentum and impulse calculator requires a lot of values, it’s still very easy to work with. As long as you have the values and you input them in the proper fields, the change in momentum calculator does the work for you. Here are the steps you should take:

• First, enter the value of the Velocity Change and choose the unit of measurement from the drop-down menu.
• Next, enter the value of the Initial Velocity and choose the unit of measurement from the drop-down menu.
• Then enter the value of the Final Velocity and choose the unit of measurement from the drop-down menu.
• After that, enter the value of the Mass and choose the unit of measurement from the drop-down menu.
• Then enter the value of the Force and choose the unit of measurement from the drop-down menu.
• Finally, enter the value of the Time Change and choose the unit of measurement from the drop-down menu.
• After entering all of these values, the impulse and momentum calculator automatically generates the results for you. This calculator gives you the values of the Impulse, Initial Momentum, and Final Momentum.

## How to calculate momentum?

Before using this momentum calculator, you must understand what momentum is first. By definition, momentum “p” is a vector which is the product of the velocity “v” and the mass “m” of any given object. Therefore, the momentum formula is:

p = m * v

We call any change which occurs in a body’s momentum impulse “J” with the formula:

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

Delta with the symbol Δ means “change.” For instance, although p refers to the instantaneous momentum, Δp represents the momentum change which happened over a specific period of time. Learning about momentum is essential because this has several practical applications.

## How to calculate impulse?

There is a simpler formula for impulse which indicates it as the product of force “F” and time “t” acting on a given body. The formula is:

J = F * t

The unit of both impulse and momentum is newton-seconds with a symbol “Ns.” In SI units, you express this unit as kg*m/s. If you’ve performed manual computation using either the impulse or momentum formula, you can check your answers using the momentum and impulse calculator. But if you want to learn the different ways to calculate impulse:

• First, you need to acquire the values of the initial momentum and final momentum. Input these values in the change in momentum calculator to get the value you need for J = Δp.
• Second, you can enter the values of velocity change and mass of a given object. You use these values in a different computation using the formula J = m * Δv.
• Finally, if you know the value of the force acting on the object, enter the values of the time change and the force. For these values, the momentum calculator uses the formula J = F * t.

This is why the calculator requires you to input several values. So it can perform the different calculations to give you the results you need.

## How do you find the initial and final momentum?

To make this easier for you to understand, let’s use an example to illustrate how to find the initial and final momentum without using the momentum calculator. For this example, let’s say that a given object with a mass of 100 kg gets uniformly accelerated from an initial velocity of 5 m s−1 to 8 m s−1 in a period of 6 seconds.

With this information, let’s find the initial and final momentum of this object. Also, let’s solve for the magnitude of force exerted on this object. The information we have is:

The initial velocity of the given object is u = 5 m/s.
The final velocity of the given object is v = 8 m/s.
The mass of the given object is m = 100 kg.
The time taken by the object to accelerate is t = 6 s.

Therefore, the equation to find the initial momentum is:

mu = 100 × 5 = 500 kg m s−1

While the equation to find the final momentum is:

mv = 100 × 8 = 800 kg m s−1

To solve for the magnitude of force exerted on the given object, use this formula:

F = mv – mu / t
= m (v-u) / t
= 800 – 500
= 300 / 6
= 50 N

After calculating with these formulas, you get the following results:

Initial momentum of the given object is mu = 500 kg m s−1.
Final momentum of the given object is mv = 800 kg m s−1.
The magnitude of the force exerted on the given object is F = 50 N.

## How do you find change in momentum with force and time?

Momentum measures a given object’s “motion content.” It’s based on the product of any given object’s velocity and mass. When velocity or mass doubles, so does the momentum. In the same way, if two objects move with the same velocity, one with double the mass of the other, this also doubles the momentum.

On the other hand, force refers to a pull or push applied to a given object which changes the object’s momentum. According to Newton’s second law of motion, force is the product of mass and acceleration. Since acceleration refers to the change in velocity divided by time, you can come up with an appropriate formula:

force = mass x (velocity / time)
= (mass x velocity) / time
= momentum / time

When you multiply both sides of the equation by time, you get the formula for momentum:

momentum = force x time