Momentum Formula

In Newtonian mechanics, Momentum Formula is the result of an object’s mass and velocity, more precisely linear momentum or translational momentum. It has both a magnitude and a direction, making it a vector quantity. If an item has mass (m) and velocity (v), then it has momentum (p). The kilogram metre per second (kg/s) is the SI unit of Momentum Formula, and it is equivalent to the newton-second. Learn about momentum formula, its definition and examples based on momentum formula in this post by Extramarks.

Momentum Definition

Momentum is a fundamental concept in physics that describes the quantity of motion possessed by an object. In simpler terms, it is a measure of how difficult it is to stop an object that is moving.

• Mathematically, momentum (p) is defined as the product of an object’s mass (m) and its velocity (v).
• Momentum is a vector quantity, which means it has both magnitude and direction. It points in the same direction as the object’s velocity.
• Momentum units are derived from mass and velocity units. The International System of Units (SI) defines momentum as kilogram meters per second.

Newton’s first law of motion states that unless an external force acts on an item in motion, it will continue to move at a constant velocity. Momentum is frequently used to evaluate and forecast the motion of objects and systems in such situations.

What is Momentum Formula?

A particle’s momentum is traditionally symbolised by the letter p. It is calculated by multiplying the particle’s mass (m) by its velocity (v). The formula of momentum is expressed as

p = mv

where,

• p is momentum
• m is mass of object
• v is velocity of object

Unit of Momentum

• The SI unit of momentum is kg.m/s
• Other unit of momentum is Newton.Second(N.s)

Conservation of Momentum

Law of Conservation of momentum states that total momentum remains constant in a closed system (one that does not interchange matter with its surroundings and is not operated on by external forces). Consider the case of two particles interacting or colliding then total momentum before and after collision is constant. This is based on Netwon’s third law of motion. It is expressed as

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

• m₁ and m₂ are mass of objects 1 and 2
• u₁ and u₂ are velocity of objects before collision
• v₁ and v₂ are velocity of objects after collision

Solved Example on Momentum Formula

Solved examples on the Momentum Formula are provided by Extramarks for practice.

Example 1: Calculate the momentum of a car with a mass of 1500 kg traveling at a velocity of 25 m/s.

Solution:

Mass (m) = 1500 kg

Velocity (v) = 25 m/s

Using the momentum formula:

p = mv

p = 1500 x 25 = 37500 kg.m/s

Example 2: A soccer ball with a mass of 0.4 kg is kicked with a velocity of 10 m/s. Calculate its momentum.

Solution:

Mass (m) = 0.4 kg
Velocity (v) = 10 m/s

p = mv

p = 0.4 x 10 = 4 kg.m/s

Example 3: Two cars collide head-on. Car A has a mass of 1200 kg and is moving at 15 m/s, while Car B has a mass of 1500 kg and is moving at 20 m/s in the opposite direction. Calculate the total momentum before and after the collision.

Solution:

Car A mass (mA) = 1200 kg, velocity (vA) = 15 m/s
Car B mass (mB) = 1500 kg, velocity (vB) = -20 m/s (negative due to opposite direction)

p_initial=m_A×v_A+m_B×v_B

p_initial =(1200kg×15m/s)+(1500kg×(−20)m/s)

p_initial =18000kg⋅m/s−30000kg⋅m/s

p_initial =−12000kg⋅m/s

Since, momentum remains conserved hence, momentum after collison will be same i.e. 12000kg⋅m/s