Unit 5: Momentum

# What is momentum?

Momentum is the degree of an object's opposition to a modification in motion. It is a vector quantity, indicating it has both size and direction. The momentum formula is p = mv, where p is momentum, m is mass, and v is velocity. This unit accounts for 12-18% of the exam weight.

# Momentum and Impulse

## Momentum

**Momentum** is a measure of an object’s resistance to a change in motion, which is defined as the product of an object’s mass and velocity. It has both magnitude and direction.

Momentum is a property of a moving object that is equal to the product of its mass and velocity.

It is a vector quantity, meaning it has both magnitude and direction.

The unit of momentum is kg m/s.

The formula for momentum is:

`p = mv`

, where p is momentum, m is mass, and v is velocity.Momentum is conserved in a closed system, meaning the total momentum of the system before a collision is equal to the total momentum after the collision.

## Impulse

**Impulse** is the change in momentum of an object over a given time period. It is the product of the force applied to an object and the time over which the force is applied.

Impulse is the change in momentum of an object over a period of time.

It is also a vector quantity.

The unit of impulse is Ns (newton-second).

The formula for impulse is:

`J = FΔt`

, where J is impulse, F is the force applied, and Δt is the time interval over which the force is applied.Impulse is equal to the area under a force-time graph.

# Conservation of Linear Momentum

Linear momentum is the product of mass and velocity of an object. According to the law of conservation of linear momentum, the total momentum of a system of objects remains constant if no external forces act on the system. This means that the sum of the momenta of all the objects in the system before a collision is equal to the sum of the momenta of all the objects after the collision.

This law is applicable to both elastic and inelastic collisions.

In an elastic collision, the total kinetic energy of the system is conserved, while in an inelastic collision, some of the kinetic energy is converted into other forms of energy, such as heat or sound.

The conservation of linear momentum is a fundamental principle in physics and is used to explain a wide range of phenomena, from the behavior of subatomic particles to the motion of planets in the solar system.

This law is also used in engineering and technology to design and analyze systems that involve the transfer of momentum, such as rockets, satellites, and automobiles.

The conservation of linear momentum is a consequence of the fundamental symmetry of nature known as translational symmetry, which states that the laws of physics are the same in all inertial reference frames.

`The total linear momentum of an isolated ststem remains constant.`

total Pinital = total Pfinal

# Collisions

Collisions occur when two or more objects come into contact with each other. The following are some important concepts related to collisions:

## Types of Collisions

There are three types of collisions:

Elastic Collisions: In an elastic collision, the total kinetic energy of the system is conserved. This means that the objects bounce off each other without losing any energy.

Inelastic Collisions: In an inelastic collision, the total kinetic energy of the system is not conserved. This means that the objects stick together after the collision and some energy is lost as heat or sound.

Perfectly Inelastic Collision: In an Perfectly Inelastic Collision, the objects stick together and travel in the same direction.

The image below represents these three types:

Collisions are an important concept in physics and have many real-world applications. Understanding the types of collisions, conservation of momentum, coefficient of restitution, and impulse can help in analyzing and predicting the behavior of objects in collisions.

# Unit 5: Momentum

# What is momentum?

Momentum is the degree of an object's opposition to a modification in motion. It is a vector quantity, indicating it has both size and direction. The momentum formula is p = mv, where p is momentum, m is mass, and v is velocity. This unit accounts for 12-18% of the exam weight.

# Momentum and Impulse

## Momentum

**Momentum** is a measure of an object’s resistance to a change in motion, which is defined as the product of an object’s mass and velocity. It has both magnitude and direction.

Momentum is a property of a moving object that is equal to the product of its mass and velocity.

It is a vector quantity, meaning it has both magnitude and direction.

The unit of momentum is kg m/s.

The formula for momentum is:

`p = mv`

, where p is momentum, m is mass, and v is velocity.Momentum is conserved in a closed system, meaning the total momentum of the system before a collision is equal to the total momentum after the collision.

## Impulse

**Impulse** is the change in momentum of an object over a given time period. It is the product of the force applied to an object and the time over which the force is applied.

Impulse is the change in momentum of an object over a period of time.

It is also a vector quantity.

The unit of impulse is Ns (newton-second).

The formula for impulse is:

`J = FΔt`

, where J is impulse, F is the force applied, and Δt is the time interval over which the force is applied.Impulse is equal to the area under a force-time graph.

# Conservation of Linear Momentum

Linear momentum is the product of mass and velocity of an object. According to the law of conservation of linear momentum, the total momentum of a system of objects remains constant if no external forces act on the system. This means that the sum of the momenta of all the objects in the system before a collision is equal to the sum of the momenta of all the objects after the collision.

This law is applicable to both elastic and inelastic collisions.

In an elastic collision, the total kinetic energy of the system is conserved, while in an inelastic collision, some of the kinetic energy is converted into other forms of energy, such as heat or sound.

The conservation of linear momentum is a fundamental principle in physics and is used to explain a wide range of phenomena, from the behavior of subatomic particles to the motion of planets in the solar system.

This law is also used in engineering and technology to design and analyze systems that involve the transfer of momentum, such as rockets, satellites, and automobiles.

The conservation of linear momentum is a consequence of the fundamental symmetry of nature known as translational symmetry, which states that the laws of physics are the same in all inertial reference frames.

`The total linear momentum of an isolated ststem remains constant.`

total Pinital = total Pfinal

# Collisions

Collisions occur when two or more objects come into contact with each other. The following are some important concepts related to collisions:

## Types of Collisions

There are three types of collisions:

Elastic Collisions: In an elastic collision, the total kinetic energy of the system is conserved. This means that the objects bounce off each other without losing any energy.

Inelastic Collisions: In an inelastic collision, the total kinetic energy of the system is not conserved. This means that the objects stick together after the collision and some energy is lost as heat or sound.

Perfectly Inelastic Collision: In an Perfectly Inelastic Collision, the objects stick together and travel in the same direction.

The image below represents these three types:

Collisions are an important concept in physics and have many real-world applications. Understanding the types of collisions, conservation of momentum, coefficient of restitution, and impulse can help in analyzing and predicting the behavior of objects in collisions.