**Momentum**

You might have often heard the word ‘momentum’. ‘Today’s youth seems to create their momentum.’ ‘There is evidence that the economy is losing its momentum.’ ‘If you do not keep improving, then you will lose momentum on your competitors one day.’

We use this term generally in our life. But have you ever thought that momentum could also be a scientific term? What is its scientific meaning, and can it be calculated like other scientific terms?

This article aims to let you know this and help you with some solved problems related to momentum. These problems will guide you in learning the way to solve problems on it.

**Momentum Meaning**

In simple language, there are several momentum meanings. It is a force that keeps an object moving or an event developing after it has started. In other words, the increase in a process’s development rate is called momentum.

It is one of the essential concepts of Physics that is also associated with your daily life. In short, every activity that involves motion is about momentum.

**Define Momentum**

It is not hard to define momentum. In the simplest form, you can define momentum as ‘mass in motion.’

It is a quantity that combines the object’s mass and its velocity. Newton defined momentum, p, of an object as the product of its mass, m, and velocity, v, i.e., the momentum formula is

p = mv

Velocity is a vector quantity. Therefore, It is also a vector quantity. It has both magnitude and direction. The direction of momentum is the same as that of speed or velocity, v. The SI unit of momentum is kg m/sec.

It is simply a quantity of motion. It is a measurable quantity because it depends upon the object’s velocity and mass, and both can be measured.

As the application of an unbalanced force creates a change in velocity, it is also possible that a force can bring a change in momentum. The force necessary to change an object’s momentum depends on the time at which the momentum is changed.

The second law of motion states that the rate of change of momentum of an object is directly proportional to the applied unbalanced force in the direction of the force.

**Factors Affecting Linear Momentum**

Take a look at the examples mentioned below to understand momentum:

**Case 1:** The weight of a cricket ball is more than the tennis ball. Suppose a player throws both the balls with equal velocity. Because of the heavy mass of a cricket ball, it requires more force to stop the cricket ball than to stop a tennis ball. Therefore, the force required to stop the ball is directly proportional to its mass.

**Case 2:** While in the case of throwing two same balls but with different velocities. You may observe that the force required to stop the ball with a higher velocity is more than that of the lower velocity ball. Hence, it is concluded that the force required to stop a moving body is directly proportional to its velocity.

From the above two cases, it is observed that momentum is affected by two factors:

- Momentum ∝ mass of the object
- Momentum ∝ velocity of the object

Therefore, an increase (or decrease) in the mass of the object increases (or decreases) the force required to stop the object (i.e., momentum).

Similarly, an increase (or decrease) in the velocity of the object increases (or decreases) the force required to stop the object (i.e., momentum).

**What is Angular Momentum?**

In terms of rotational motion, angular velocity is the rotational analogue of linear velocity. Similarly, angular momentum is the rotational analogue of linear momentum. Simply put, the degree upto which a body can rotate is its angular momentum.

Angular momentum (L) is elucidated as the product of angular velocity () and moment of inertia (I).

Hence,

Angular momentum, L = I

In terms of linear momentum, you can write angular momentum as

L = r x p

Where L = angular momentum, r = length vector, and p = linear momentum

Angular momentum is a vector quantity with magnitude and direction like linear momentum. The SI unit of the angular momentum is kg m^{2}/sec.

**Importance of Momentum in Everyday Life**

Every moving body possesses momentum. Some real-time examples can help you to understand this:

- You use the word momentum frequently in your daily life. Like, I know exercise has great momentum on one’s fitness. If you do not exercise regularly, the body will have negative momentum, which will be hard to remove!
- Road accidents at high speed are worse than at low speed. It is because the impact of momentum when a high-speed vehicle collides with another vehicle is far more than that of low speed. As a result, the casualty rate increases.
- While watching a sport, you often comment that this sports team has a lot of momentum.
- Although the size of a bullet is small, it acquires a high velocity. Hence, it impacts a high momentum on the body.
- A student running a race with some velocity has high momentum. The student running in a race represents a mass moving with velocity.

**Law of Conservation of Momentum**

Let two objects of different masses moving with different velocities collide. Then, for an ideal collision, the sum of momenta of the two (or more) objects (before the collision) is equal to the sum of momenta of those objects after the collision, provided there is no external biased force acting on them. It is called the law of conservation of momentum.

Mathematically,

m_{A}u_{A} + m_{B}u_{B} = m_{A}v_{A} + m_{B}v_{B}

Where m_{A} = mass of object A, u_{A} = initial velocity of A, and v_{A} = final velocity of A;

m_{B} = mass of object B, u_{B} = initial velocity of B, and v_{B} = final velocity of B.

**Some Solved Problems of Momentum**

**Example 1.** What will be the momentum when a ball of mass 200g moves with a velocity of 5m/sec?

**Answer:** Here, mass of the object, m = 200g = 0.2 kg

Velocity of the object = 5m/sec

According to the momentum formula,

p = mv

⇒ p = 0.2 x 5 = 1

Hence, the momentum will be 1kg m/sec.

**Example 2.** Calculate the change in momentum when a car of weight 1500 kg moves with a velocity of 36 km/h to 72 km/h.

**Answer:** Here, initial velocity, u = 36 km/h = 10 m/sec

And final velocity, v = 72 km/h = 20 m/sec

The car having mass, m = 1500 kg

According to the change in momentum formula,

Change in momentum, Δp = m (v – u)

⇒ Δp = 1500 x (20 – 10) = 15000

Hence, the change in momentum is 15000 kg m/sec.

**Example 3.** A metallic rod of mass 200 kg rotates about its axis at an angular velocity of 100m/sec. If the radius of the rod is 0.5m, find the angular momentum of the metallic rod about its axis.

**Answer:** Here, radius of the rod, r = 0.5m

The mass of the rod, m = 200kg

Angular velocity, = 100m/sec

As the metallic rod is cylinder in shape, moment of inertia, I = (m r^{2})/2

⇒ I = (200 x 0.5 x 0.5)/2 = 25 kg m^{2}

So, according to the angular momentum formula,

L = I

⇒ L = 25 x 100 = 2500

Hence, the angular momentum is 2500 kg m^{2}/sec.

**Conclusion**

You are now well-informed about the momentum and related terms from the above discussion. It is concluded that the momentum meaning, in simple words, is ‘the force that makes something move faster and faster.’ If you talk about life, momentum is an ability that lets you move forward without holding you back.

In Physics, momentum plays an important role. It describes the relationship between mass, speed, and direction. It also talks about the force required to stop objects or let them in motion.

**Frequently Asked Questions**

**Q1.**** Why does a gunman get a jerk on firing a bullet?**

**Answer:** According to the law of conservation of momentum,

The total momentum of a bullet = The total momentum of a gun

A gunman fires a bullet and produces momentum in the forward direction. As an act of the law of conservation of momentum, the gun will produce an equal momentum in the backward direction. Therefore, the gunman gets a jerk on firing a bullet.

**Q2.**** Why does a karate player easily break the piles of tiles with a single blow of his hand?**

**Answer:** Karate players hit their hands with a greater velocity on piles of tiles. As a result, the magnitude of momentum increases and results in a greater effect. Another reason behind their action is the large applied force in a very short time. It gives birth to impulses between them. Therefore, the tiles break easily.

**Q3.**** Airbags are used to protect us during a car collision. Give a reason.**

**Answer: **Force and time are inversely proportional to momentum. So, if time is increased, force is decreased. The airbags are designed in such a way that they can increase the time required to stop the body’s momentum during a collision. As a result, they reduce the impact of force and minimise the body’s injuries.

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