Linear Momentum: Relation with 2nd Law of Newton

Abstract

Momentum is the quantity of motion due to its mass and velocity. Mathematically expressed as p=mv with SI unit newton second Ns. When a force acts on a body, it produces an acceleration in the body and will be equal to the rate of change of momentum of the body.

It can be written as F x t=m v_f-m v_i. The change in momentum amounts to the product of force and the time for which force is applied. This kind of second law is more general than the F =ma since it can easily be extended to deal with changes as the body accelerates.

The momentum of a system depends upon its mass and velocity. If no unbalanced or net force acts upon a system, then its momentum remains constant. Therefore, this is the conservation of momentum.

Definition of Momentum

The momentum of a body is the quantity of motion it has due to its mass and velocity.

We understand the fact that moving item possesses a quality by means of which it puts in a force on anything that tries to stop it. The faster the object is moving, the more difficult is to stop it. Similarly, if two items move at the exact same speed, then it is more difficult to stop the massive of the two.

This quality of the moving body was called the quantity of motion of the body, by Newton. This term is now called linear momentum of the body and is specified by the relation.

Mathematical Form

Linear momentum = p = mv

ln this expression, v is the speed of the mass m. Direct momentum is, therefore, a vector quantity and has the direction of speed.

SI Unit

The SI unit of momentum is kg metre – per second (kgms^-1). It can likewise be expressed as newton second(Ns).

Further Reading: Electric Current - SI Unit, Conventional Direction of Flow & More

Momentum and Newton’s Second Law of Motion

Statement

When a force acts on a body, it produces an acceleration in the body and will be equal to the rate of change of momentum of the body.

Explanation

Consider a body of mass m moving with an initial velocity v_i. Suppose an external force F acts on it for time t after which velocity ends up being v_f. The acceleration produced by this force is given by

a = v_f– v_i/ t

By Newton’s 2^nd law of motion acceleration, a is

a = F/m

Comparing the two values of acceleration

F/m= v_f– v_i/ t

Now,

F x t=mv_f-mv_i

Where

m v_{i –>}initial momentum
mv_{f –>} final momentum

The change in momentum amounts to the product of force and the time for which force is applied. This kind of the second law is more general than the type F =ma since it can easily be extended to account for changes as the body accelerates when its mass also alters. For example, as a rocket speeds up, it loses mass because its fuel is burnt and ejected to offer higher thrust.

MCQs about Linear Momentum

What is the mathematical expression for linear momentum?
- A) p = ma
- B) p = mv
- C) p = F × t
- D) p = m^2v
What is the SI unit of momentum?
- A) Newton (N)
- B) Meter per second squared (m/s^2)
- C) Kilogram meter per second (kg·m/s)
- D) Kilogram meter per second squared (kg·m/s^2)
Which law of motion relates force to the rate of change of momentum?
- A) Newton’s First Law
- B) Newton’s Second Law
- C) Newton’s Third Law
- D) Law of Conservation of Momentum
According to Newton’s Second Law, what is the relationship between force and acceleration?
- A) F = mv
- B) F = ma
- C) F = pt
- D) F = mv^2
What does the change in momentum of a body depend on?
- A) Time only
- B) Force only
- C) Mass and velocity
- D) Acceleration only
What is the direction of momentum?
- A) Opposite to velocity
- B) Opposite to acceleration
- C) Same as velocity
- D) Perpendicular to velocity
Which term did Newton use for the “quantity of motion” of a body?
- A) Motionality
- B) Velocity
- C) Momentum
- D) Inertia
What is the formula for acceleration according to Newton’s Second Law?
- A) a = F × t
- B) a = mv
- C) a = vf – vi / t
- D) a = F / m
What does the conservation of momentum state?
- A) Momentum remains constant if no force is applied.
- B) Momentum increases with time.
- C) Momentum decreases with velocity.
- D) Momentum decreases with mass.
Which law of motion deals with changes in momentum as a body accelerates?
- A) Newton’s First Law
- B) Newton’s Second Law
- C) Newton’s Third Law
- D) Law of Conservation of Momentum
What does F x t represent in the context of momentum?
- A) Initial momentum
- B) Final momentum
- C) Change in momentum
- D) Total momentum
What is the relationship between force, time, and change in momentum?
- A) F = Δp / t
- B) F = Δp × t
- C) F = Δp + t
- D) F = Δp – t
What is the SI unit of momentum?
- A) Kilogram meter per second (kg·m/s)
- B) Newton per second (N/s)
- C) Newton meter per second squared (N·m/s^2)
- D) Kilogram meter per second squared (kg·m/s^2)
According to Newton’s Second Law, what is the relationship between force and acceleration?
- A) Directly proportional
- B) Inversely proportional
- C) No relationship
- D) Constant relationship
Which quantity of motion is specified by the relation p = mv?
- A) Kinetic energy
- B) Potential energy
- C) Linear momentum
- D) Angular momentum

Summary

In summary, linear momentum, defined as the product of an object’s mass and velocity, is a crucial concept in physics, quantifying the motion of an object. Described by the equation $p = m v$ , where $p$ represents momentum, $m$ signifies mass, and $v$ denotes velocity, its SI unit is the newton second (Ns).

This momentum is intrinsically linked with Newton’s Second Law of Motion, which states that when an external force acts on an object, it produces an acceleration equal to the rate of change of momentum. This relationship is expressed mathematically as $F \times t = m v_{f} - m v_{i}$ , where $F$ represents force, $t$ denotes time, $v_{f}$ is the final velocity, and $v_{i}$ is the initial velocity.

Further Reading: Blackbody and Blackbody Radiation

Furthermore, the conservation of momentum holds true if no unbalanced force acts upon a system, signifying its significance in physics. By understanding these principles, one gains insight into how forces influence the motion of objects and how momentum is conserved in various scenarios.