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Linear momentum is a fundamental concept in physics that describes the motion of an object in terms of its mass and velocity. It is often referred to as “momentum” and is represented by the symbol “p”. Linear momentum is a vector quantity, meaning it has both magnitude and direction.

The linear momentum of an object is defined as the product of its mass (m) and velocity (v):

p = m x v

Where:

p is the linear momentum of the object,

m is the mass of the object, and

v is the velocity of the object.

## Key Points about Linear Momentum

- Conservation of Linear Momentum: According to the principle of conservation of linear momentum, the total momentum of a system remains constant if no external forces act on it. This principle is derived from Newton’s third law of motion, stating that for every action, there is an equal and opposite reaction. This conservation law has various applications, from understanding collisions to analysing rocket propulsion.
- Impulse: Impulse is the change in momentum of an object. It is equal to the force applied to an object multiplied by the time interval over which the force acts. Mathematically, impulse (J) is given by the equation J = F x Δt, where F is the applied force and Δt is the time interval.

- Momentum and Newton’s Laws: Linear momentum plays a crucial role in Newton’s laws of motion. Newton’s second law states that the rate of change of momentum of an object is equal to the net force applied to it. It can be expressed as F = Δp / Δt, where F is the net force, Δp is the change in momentum, and Δt is the time interval.

### What is the SI unit of Linear momentum

The SI unit of momentum is kilogram-metre per second (kg·m/s). However, momentum can also be expressed in other units, such as gram-centimetre per second (g·cm/s) or newton-second (N·s), depending on the context.

Now, when a net force is applied, the velocity of the object changes and when velocity changes, its momentum also changes.

So, net force is nothing but the rate of change of momentum.

Therefore,

Net force = (p2 – p1)/t

where, p1 = initial momentum, p2 = final momentum and t = time taken

The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force.

### Solved Examples on Linear Momentum Formula

**Example 1**: A car of mass 1000 kg is initially at rest. It accelerates uniformly and reaches a velocity of 20 m/s in 10 seconds. What is the linear momentum of the car at this point?

**Solution: **

Given:

Mass of the car (m) = 1000 kg

Initial velocity (u) = 0 m/s

Final velocity (v) = 20 m/s

Time (t) = 10 s

Using the formula for linear momentum: p = m x v

Substituting the given values:

p = 1000 kg x 20 m/s

p = 20,000 kg·m/s

Therefore, the linear momentum of the car at this point is 20,000 kg·m/s.

**Example 2: **A bullet with a mass of 0.02 kg is fired from a rifle with a velocity of 400 m/s. What is the linear momentum of the bullet?

**Solution: **

Given:

Mass of the bullet (m) = 0.02 kg

Velocity of the bullet (v) = 400 m/s

Using the formula for linear momentum: p = m x v

Substituting the given values:

p = 0.02 kg x 400 m/s

p = 8 kg·m/s

Therefore, the linear momentum of the bullet is 8 kg·m/s.

**Example 3: **Two objects with masses 2 kg and 3 kg, respectively, are initially at rest. They collide and stick together. What is their final velocity after the collision?

**Solution: **

Given:

Mass of object 1 (m1) = 2 kg

Mass of object 2 (m2) = 3 kg

Initial velocity of both objects (u1 and u2) = 0 m/s

Since the objects stick together after the collision, their final velocity is the same. Let’s call it v.

Using the principle of conservation of linear momentum:

(m1 u1) + (m2 u2) = (m1 + m2) x v

Substituting the given values:

(2 kg x 0 m/s) + (3 kg x 0 m/s) = (2 kg + 3 kg) x v

0 = 5 kg x v

Since the left side of the equation is zero, the final velocity (v) is also zero.

Therefore, the final velocity of the objects after the collision is 0 m/s.

## Frequently Asked Questions on Linear Momentum Formula

### What is linear momentum?

Linear momentum, often referred to as momentum, is a fundamental concept in physics that describes the motion of an object in terms of its mass and velocity. It is the product of an object's mass and its velocity.

### What is the formula for linear momentum?

The formula for linear momentum is: p = m x v Where p is the linear momentum, m is the mass of the object, and v is its velocity.

### What are the units of linear momentum?

The units of linear momentum are kilogram-metre per second (kg·m/s) in the International System of Units (SI).

### What is the principle of conservation of linear momentum?

The principle of conservation of linear momentum states that the total linear momentum of an isolated system remains constant if no external forces act on it. In other words, the total momentum before an event or interaction is equal to the total momentum after the event or interaction, as long as no external forces are present.

### How is linear momentum related to force?

Linear momentum is related to force through Newton's second law of motion. According to the law, the rate of change of linear momentum of an object is equal to the net force acting on it. Mathematically, it can be expressed as F = Δp/Δt, where F is the net force, Δp is the change in momentum, and Δt is the change in time.

### What is the difference between linear momentum and kinetic energy?

Linear momentum describes an object's motion in terms of its mass and velocity, while kinetic energy represents the energy of an object due to its motion. Momentum is a vector quantity, while kinetic energy is a scalar quantity.

### Can the linear momentum of an object be negative?

Yes, the linear momentum of an object can be negative. The sign of momentum indicates the direction of motion. Positive momentum indicates motion in one direction, while negative momentum indicates motion in the opposite direction.