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In this blog, we will understand and learn about the Laws of Motion in detail.

<h2 id="content-id-1934-0">Laws of Motion</h2>

Newton’s First Law of Motion:

A body continues in its state of rest or of uniform motion in a straight line unless an external force acts on it. It is based on Galileo’s law of inertia. Inertia is the property of a body by virtue of which the body opposes any change in its state of rest or of uniform motion along a straight line.

Inertia of Rest: When a bus or train, initially at rest, starts to move suddenly, the passengers sitting in it jerk in a backward direction due to their inertia of rest. The dust particles come out from a carpet when it is beaten with a stick due to their inertia of rest. A passenger jumping out from a moving bus or train is advised to jump in forward direction and run forward for a short mile due to inertia of rest.

Inertia of Motion: When a running bus or train stops suddenly, the passengers sitting in it jerk in forward direction due to inertia of motion.

Momentum: The momentum for any moving body is equal to the product of its mass and its velocity. p = m × v

Conservation of Linear Momentum: The linear momentum of a system of particles remains conserved if the external force acting on the system is zero. Rocket propulsion and engine of jet airplane work on the principle of conservation of linear momentum. In a rocket, ejecting gas exerts a forward force which helps in accelerating the rocket upward.

Newton’s Second Law:

The rate of change of momentum of a body is directly proportional to the force applied on it and change in momentum takes place in the direction of applied force. 

F= △p/△t = m△v/△t = ma

Newton’s Third Law:

It states that “For every action, there is an equal and opposite reaction and both act on two interacting objects.” Ex. Rocket is propelled by the principle of Newton’s third law of motion.

<h2 id="content-id-1934-1">Equations of Motion </h2>

Derivation of First Equation of Motion:

We know that the rate of change of velocity is the definition of acceleration. Let us assume a body that has a mass “m” and initial velocity “u”. Let after time “t” its final velocity becomes “v” due to uniform acceleration “a”. Now we know that:

Acceleration = (Final Velocity - Initial Velocity)/Time Taken a = (v - u)/t or at = v - u v = u + at

Derivation of Second Equation of Motion:

Let the distance be “s”. Distance = Average velocity × Time. Also, Average velocity (u + v)/2 Distance (s) = (u + v)/2 × t Also, from v = u + at s = (u + u + at)/2 × t = (2u + at)/2 × t s = (2ut + at²)/2 = 2ut/2 + at²/2 Or s = ut + ½ at²

Derivation of Third Equation of Motion:

We have, v = u + at. Hence, we can write t = (v - u)/a Also, we know that, Distance = average velocity × Time Therefore, for constant acceleration we can write: Average velocity = (final velocity + initial velocity) / 2 = (v + u) / 2 Hence, Distance (s) = [(v + u)/2]×[(v - u)/a] Or s = (v2-u2)/2a Or 2as = v2 - u2 Or v2=u2+2as

Motion Under Gravity:

Free fall: A body released near the surface of the earth is accelerated downward under the influence of force of gravity. In the absence of air resistance, all bodies fall with the same acceleration near the surface of earth. The motion of the body falling towards the earth from a small height is called free fall.

Equations of motion under freely falling body:

<ol>
	<li>v = u + gt</li>
	<li>s = ut + 1/2 gt2</li>
	<li>v2 – u2 = 2gs</li>
</ol>

For a body falling freely under the action of gravity, g is taken positive. For a body thrown vertically upward, g is taken negative When a body is just dropped, u = 0 For a body thrown vertically up with initial velocity u: 

<ol>
	<li>Maximum height reached, h = u2 /2g</li>
	<li>Time of ascent = time of descent = u/g</li>
	<li>Total time of flight = 2u/g</li>
	<li>Velocity of particle at the point of projection = u Velocity attained by a body dropped from height h</li>
</ol>

V= √2gh

<h2 id="content-id-1934-2">Relative velocity</h2>

This is the velocity of an object relative to some other object which might be stationary, moving slowly, moving with same velocity, moving with higher velocity or moving in opposite direction.

If initial position of two objects A and B are xA (0) and xB (0), the position at time t will be,

<ul>
	<li>x A (t) = xA (0) + vA t</li>
	<li>x B (t) = xB (0) + vB t</li>
</ul>

Displacement from object A to B, [xB (0) - xA (0)] + (vB - vA )t

Velocity of B relative to A = vBA = vB - vA

Velocity of A relative to B = vAB = vA - vB

<h2 id="content-id-1934-3">Motion in two dimensions</h2>

To understand the motion in two dimensions, let’s first understand the scalar and vector quantities.

Scalar Quantities: The physical quantities which are completely specified by their magnitude or size alone are called scalar quantities. Examples; Length, mass, density, speed, work, etc.

Vector Quantities: Vector quantities are those physical quantities which are characterized by both magnitude and direction. Examples; Velocity, displacement, acceleration, force, momentum, torque etc.

Characteristics of Vectors: 

Following are the characteristics of vectors:

<ol>
	<li>They possess both magnitude and direction.</li>
	<li>They do not obey the ordinary laws of Algebra.</li>
	<li>They change if either magnitude or direction or both changes.</li>
	<li>They are represented by bold-faced letters or letters having arrows over them.</li>
</ol>

<h2 id="content-id-1934-4">Projectile motion</h2>

A body moving horizontally as well as vertically under the action of gravity simultaneously is called a projectile. The motion of a projectile is called projectile motion. The path followed by a projectile is called its trajectory. Examples of projectile motion are.

<ol>
	<li>Kicked or thrown balls</li>
	<li>Jumping animals </li>
	<li>A bomb released from a bomber plane</li>
	<li>A shell of a gun.</li>
</ol>

Analysis of Projectile Motion:

Let us consider a body of mass m, projected at an angle θ with the horizontal with a velocity V0 . A common example would be throwing a ball in air. When we talk about motion in two dimensions in practical lives the role of gravitational forces come in and hence body experiences a downward acceleration equal to g (9.8 m/s2 ).

<ol>
	<li>The value of g remains constant throughout the motion.</li>
	<li>The effect of air resistance is negligible.</li>
	<li>The rotation of earth does not affect the motion.</li>
</ol>

We studied about the motion in one and two dimensions and relative velocity in this blog. In the next blog we will learn about thermal properties of matter.

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