[Physics Class Notes] on Newton's Second Law of Motion Pdf for Exam

Newton’s second law of motion is related with the first law of motion. It gives the quantitative definition of force. Mathematically, it describes the causes and effects of force and changes in the motion of an object. Before understanding the equation of Newton’s second law of motion which deals with the force, mass, and acceleration of an object, let’s have a look at the three laws of motion.

Well, it’s a common fact that the students are most familiar with Newton’s law of motion, how an apple fell from the tree and resulted in a massive discovery in the history of mankind. Thanks to Sir Issac Newton for that as it has been of use for years now and has helped in the development of many new innovations. Moving forward the students are taught these concepts to make them familiar with the concepts and make their way easier for further studies.

The students are provided with all the related study material and resources on ’s website for free. The study material is available for classes 1 to 12 in the form of notes, revision notes, worksheets, sample papers, NCERT Solutions, NCERT Exemplar solutions, and other material for the students to make use of them while preparing for the exam and to clear their concepts and doubts well with ease.

The Three Laws of Motion

Newton’s 1^st law: It is also called the law of inertia. The statement depicts, “if a body is in the state of absolute rest, or in uniform motion, it will continue to remain likewise, provided it is acted upon by a foreign force.”

Newton’s 2^nd law: The statement depicts, “the rate of change of momentum of a body is directly proportional to the external force applied to the body. Further, the momentum of the body happens to be in the direction where the force is exerted.”

Newton’s 3^rd law: The statement depicts, “no matter what is the action, according to this phenomenon, always an equal & opposite reaction abides for it”.

Newton’s Second Law Statement

Newton’s first law statement, “unless a body is acted by a foreign force, it abides in its state of rest, or of uniform motion.” So, the question arises, what happens to your body when an external force is applied to it? This answer is provided by Newton’s second law of motion.

According to Newton’s second law of motion, force acting on a body is equal to the rate of change of momentum. For a body with a constant mass ‘m’, force is given by,

F = ma

Where,

a = acceleration produced in the body.

The above equation describes that, if the force is doubled, the acceleration also gets doubled, and if mass is doubled, acceleration becomes half.

Sir Issac Newton published his works about the laws of motion in 1687, in his book “Philosophiæ Naturalis Principia Mathematica” (Mathematical Principles of Natural Philosophy), in which he described how objects with different masses move under the influence of applied force.

The first study regarding the laws of motion was done by Galileo Galilei. Based on Galileo’s experiments, all objects accelerate at the same rate regardless of their size and mass. Rene Descartes also published some laws regarding the motion of objects in 1644. Later Sir Issac Newton expanded the works of both these scientists and formulated his laws of motion.

Acceleration and Velocity

Newton’s second law of motion describes that, when a force is applied to an object, it produces acceleration in the object (i.e rate of change of velocity). For an object at rest, the applied force produces acceleration in the object and makes the object move in the direction of applied force.

For an object which is already in motion, the direction of the applied force matters to determine its state. If external force is applied in the direction in which the object is moving, the acceleration of the object increases. If external force is applied in the direction opposite to the motion of the object, the acceleration of the object decreases and finally comes to stop.

Force and acceleration are vector quantities, i.e they have both magnitude and direction. Multiple forces can also act in a body at a time.

Hence,

[Sigma]F = ma

Where;

[Sigma]= vector sum of all the forces acting on a body (net force).

For Changing the Mass

For this let’s assume that we have a car at a point (0) which is defined by the location X₀ and time t₀. The car has a mass of m0 and travels with a velocity of v₀. Here, after being subjected to a force ‘F’, the car starts to move to point 1, defined by location X₁ and the time by t₁. The mass and the velocity of the car changes during the travel to values m1 and v₁ respectively. Thus, Newton’s second law helps to determine the new values of m₁ and v₁ if we already know the value of the acting force.

From the difference of point 1 and point 0, an equation for the force acting on the car is formed as follows:

F=m₁v₁−m₀v₀t₁−t₀

F=m₁v₁−m₀v₀t₁−t₀

Now, let’s assume the mass to be constant here. This assumption is helpful for a car as the only change in the mass would be the fuel burned while moving between point “1” and point “0”. Here, the weight of the fuel is probably very small as compared to the rest of the car, especially looking at the small changes in time. Meanwhile, if we discuss the flight of a bottle rocket, then the mass does not remain constant here, and only the changes in momentum can be looked at.

For Constant Mass

For a constant mass, Newton’s second law can be equated as follows:

F=mv₁−v₀t₁−t₀

F=mv₁−v₀t₁−t₀

We know, acceleration is defined as the change in velocity which is divided by the change in time.

The second law then decreases to a more common form as follows:

F=ma

The above equation conveys to us that an object will accelerate if it is subjected to an external force. While the amount of force is directly proportional to the acceleration and inversely proportional to the object’s mass.

Application of Newton’s Second Law of Motion

Some applications of Newton’s second law of motion are mentioned below:

1. Kicking a Ball

When we kick a ba
ll we apply some force in it, and in a specific direction. The ball moves in this direction. If the applied force is more the distance covered by the ball will be more, and if the applied force is less the distance covered by the ball will be less.

2. Pushing a Cart

Pushing an empty card is easy as compared to pushing a loaded cart; this is because if the mass of an object is more, a large amount of force will be needed to move it.

3. Two People Walking

If two people of different masses work together, the one with the heavier mass will walk slower as compared to the one with the lighter mass. This is because more acceleration is produced by the lightweight person.

Second Law of Motion Examples

Some of Newton’s second law of motion examples is mentioned below:

• Pushing or pulling an empty cart is easy as compared to a loaded cart because the loaded cart has more mass.

• If the same amount of force is applied to move a car and a bike, the acceleration of the bike will be more because it has less mass than the car.

• When a ball drops on the ground, it exerts a downward force on the ground, and in reaction to it the ground exerts an equal upward force on the ball, thus making it bounce.

• Stopping a moving ball requires force.