The article discusses about what is change in momentum and formulas about how to find change in momentum.

**The change in momentum is a difference in motion. When an object is in motion, strikes, or collides with another object, the exerted force accelerates an object by varying its motion. The change in momentum is calculated using the Impulse formula or conservation of momentum. **

The moving object is said to be in momentum. **The amount of momentum gained by an object is proportional to its mass and velocity together.** Hence, the change in one quantity can cause a change in momentum. That means, if you increase or decrease an object’s mass, then its momentum changes. Similarly, the momentum also changes when you increase or decrease its velocity.

The change in velocity means an object is accelerating, and we have learned that acceleration is caused by force. So *greater the acceleration caused by force, the greater its change in momentum!!!*

Suppose an object is at rest or does not have momentum, then it requires sufficient force to overcome the friction so that an object moves with some momentum. If an object is already in momentum and force is applied in the opposite direction, its momentum will decrease. But If force applies in the same direction, then momentum will increase.

**A large force exerted over a short time causes a significant change in momentum**. If the force is small but exerted over a long time, a significant change in momentum also occurs. That means when a force applies to an already gained momentum object for a certain period of time, its momentum changes.

**Change in Momentum Examples**

The change in momentum examples explains how momentum changes when a force is acted upon.

**Long Jump**

To attain momentum before jumping, the athlete runs a certain distance. Once the athlete gains some momentum after running, they apply force on the ground to jump that changes its momentum, and the athlete jumps forward. After the jump, the athlete needs to apply a large force again on the ground to stop their motion – which changes their momentum again.

**Hitting a Ball**

The ball gains momentum when thrown by the bowler during sports like cricket or baseball. When a batter hits the ball with a bat, the applied force to the ball changes its momentum, and then a ball moves in the direction of an applied force. The ball’s momentum changes again when it is stopped or caught by the fielder.

**Driving Vehicle**

Driving a vehicle such as a car or truck involves a continuous change in momentum. We apply a force on its accelerating paddle to speed up the vehicle. To stop the vehicle suddenly, we apply a force on its brake paddle, which changes the vehicle’s momentum as per applied force.

**Football or Rugby**

In football or rugby, the striker accumulates maximum momentum when he dribbles or carries the ball near the goal coast by bypassing other players. The defenders near the goal coast then try to stop or change the striker’s momentum by tackling him.

**Playground Slides**

When children start sliding on the playground slide from height, they achieve momentum downwards. But the friction present on the playground slide surface changes the momentum of sliding children by opposing their motion, preventing them from falling at the end of the slide.

Read more about Momentum Examples

**Change in Momentum Formula**

The change in momentum formula is calculated using Newton’s second law of motion and kinematics equations of motion.

**Newton’s second law displays that an object accelerates when a force applies. Since the force applied for a specific time interval changes an object’s motion, it also causes a change in momentum. The product of force and time interval is termed as ‘impulse’, which measures the change in momentum. **

The **first kinematics equation of motion** is,

v_{f} = v_{i} + at

v_{f}– v_{i} = at

As per** Newton’s second law**, F = ma, a = F/a

v_{f}-v_{i}=(F/m)*t

m(v_{f}– v_{i}) = Ft

mΔv=Ft

Whereas RHS in the above equation is termed as ‘**Impulse’** (denoted by J) and LHS is the formula of **Momentum Change** (ΔP)

Therefore, we can also write as,

J=Ft=mΔv=ΔP…………. (*)

Impulse = Change in Momentum

The equation (*) is also known as ‘**Impulse –Momentum change equation’**.

*The more significant the impulse, the more significant the momentum change.*

The strength of force applied to an object depends on how long it acts. The concept of impulse quantifies the effect of force.

Read more about Kinematics Equations.

**Suppose a striker having a mass of 40kg dribbles the football at 10m/s. When he approaches the defender in 0.10sec, he dribbles the football at high speed, such as 15m/s, to pass the defender successfully. **

**What is the initial momentum of the striker?**

**What is the final momentum of the striker when he is approached by the defender?**

**What is the change in momentum of the sticker? **

**How much force is applied by the defender to stop the striker? **

**Calculate Impulse applied by the defender. **

** Given**:

m = 40kg

v_{i }= 10m/s

v_{f} = 15m/s

t = 0.10s

** To Find**:

- P
_{i}=? - P
_{f}=? - ΔP =?
- F =?

** Formula**:

- P = mv
- ΔP = P
_{f}–P_{i} - Ft = ΔP

** Solution**:

The initial momentum of a striker is calculated as,

P_{i} = mv_{i}

P_{i} = 40 x 10

P_{i }= 400

**The initial momentum of striker is 400kg.m/s**

The final momentum of a striker is calculated as,

P_{f }= mv_{f}

P_{f }= 40 x 15

P_{f} = 600

**The final momentum of striker is 600kg.m/s**

The change in momentum of a striker is calculated as,

ΔP = P_{f} –P_{i}

ΔP = 600 – 400

ΔP = 200

**The change in momentum of a striker is 200kg.m/s.**

The force applied by the defender to stop the striker is calculated using the impulse-momentum Change formula.

Ft = ΔP

Substituting all values,

F(0.10) = 200

F = 200/0.10

F = 2000

**The force ****applied by the defender is 2000N.**

The impulse by defender is calculated as,

J = Ft

J = 2000 x 0.10

J = 200

**The impulse by defender on striker is 200N.s.**

**How to Calculate Momentum Change?**

The momentum change is calculated using the law of conservation of momentum.

**When an external force acts on an object, we can compute its momentum change by impulse formula. But when there is no external force, the total momentum of colliding objects remains the same. That’s how we can calculate the momentum change due to collision using conservation of momentum. **

Suppose two objects have a momentum P_{1} and P_{2} due to their masses m_{1} and m_{2} and velocity u_{1} and u_{2}. Due to collision, their momentum changes to P_{1’} and P_{2’} since their velocity changes to v_{1} and v_{2}.

As per **conservation of momentum,**

m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}

Since we want to calculate change in momentum, rearranging terms m1 on LHS and m2 on RHS,

m_{1}u_{1} – m_{1}v_{1} = m_{2}u_{2} – m_{2}v_{2}

P_{1f}– P_{1i} = P_{2f}-P_{2i}

ΔP_{1} = ΔP_{2}

Momentum change in object 1 = Momentum change in object 2

Read more about Momentum after Collision

**When two balls have masses 5kg and 3kg moving towards each other at 8m/s and 15m/s, respectively, and after the collision, if the first ball moves away with a velocity of 5m/s. **

**Calculate the change in momentum of the first ball**

**Calculate the change in velocity of the second ball after the collision. **

** Given**:

m_{1} = 5kg

m_{2} = 3kg

u_{1} = 8m/s

u_{2} = 15m/s

v_{1} = 5m/s

** To Find**:

- ΔP
_{1}=? - v
_{2}=?

** Formula**:

- ΔP
_{1}= P_{1f}– P_{1i} - m
_{1}u_{1}– m_{1}v_{1}= m_{2}u_{2}– m_{2}v_{2}

** Solution**:

The change in momentum of first ball is calculated as,

ΔP_{1} = P_{1f}– P_{1i}

ΔP1 = m_{1}u_{1} – m_{1}v_{1}

Substituting all values,

ΔP_{1} = 5 x 8 – 5 x 5

ΔP_{1} = 40 – 25

ΔP_{1} = 25

**The momentum change of first ball is 25kg.m/s**

The velocity change of second ball after collision is calculated as,

m_{1}u_{1} – m_{1}v_{1} = m_{2}u_{2} – m_{2}v_{2}

Substituting all values,

25 = 3 x15 – 3v_{2}

25 = 45 – 3v_{2}

v_{2 }= -20/3

v_{2} = -6.66

**The velocity change of the second ball is -6.6m/s.**

Read more about Momentum Before Collision.