[Physics Class Notes] on Laws of Motion Pdf for Exam

Isaac Newton discovered the Laws of Motion. Newton’s laws of motion explain the connection between a physical object and the forces acting upon it. By understanding the concept, it provides all the information about the basis of modern physics. After the development of the three laws of motion, Newton revolutionized science. Newton’s three laws together with Kepler’s Laws explained the concept of planets moving in elliptical orbits rather than in circles. Although Newton’s laws of motion may seem so general today, they were considered revolutionary centuries ago. Newton’s three laws of motion help someone understand how objects behave when standing still, when moving and when forces act upon them. Sir Newton’s three laws are Newton’s First Law: Inertia, Newton’s Second Law: Force, Newton’s Third Law: Action & Reaction.

Newton’s First Law

Newton’s First Law states that ‘An object at rest remains at rest, and an object in motion remains in motion at a constant speed and in a straight line unless acted on by an unbalanced force’. This law describes that every object will remain at rest or in uniform motion in a straight line unless forced to change its state by the action of an external force. The tendency of an object to resist changes in a state of motion is inertia. There will be a net force on an object if all the external forces cancel each other out. If this happens, then the object will maintain a constant velocity. If the Velocity remains at zero, then the object remains at rest. If any external force acts on an object, the velocity will change because of the force applied. An example of the First law of motion is : The motion of a round ball falling down through the atmosphere, A rocket being launched up into the atmosphere.

Newton’s Second Law

Newton’s Second Law states that ‘The acceleration of an object depends on the mass of the object and the amount of force applied’. This law defines a force to be equal to a change in momentum (mass times velocity) per change in time. Momentum is described as the mass m of an object times its velocity V. Example of the second law of motion is: An aircraft’s motion resulting from the aerodynamic force, aircraft thrust and weight.

Newton’s Third Law

Newton’s Third Law states that ‘Whenever one object implies a force on a second object, the second object implies an equal and opposite force on the first’. This law defines that for every action in nature there is an equal and opposite reaction. If object A applied a force on object B, object B will also apply an equal and opposite force on object A. In other words, it can be said that forces result from interactions. An example of the third law of motion is: The motion of a jet engine produces thrust and hot exhaust gasses flow out the back of the engine, and a thrusting force is produced in the opposite direction.

Derivation of First Equation of Motion

Let’s Consider a body of mass m having initial velocity u.

Let after time be t its final velocity becomes v due to uniform acceleration a.

Now it is defined as:

Acceleration = Change in velocity / Time taken

Acceleration = (Final velocity – Initial velocity) / Time taken

 a = (v – u) / t

 a t = v – u

or  v = u + at

This describes the first equation of motion.

Derivation of Second Equation of Motion

As it is defined, the Second equation of motion: s = ut + (1/2) at²

Let’s take the distance traveled by the body be s.

Now:

Distance = Average velocity x Time

Also, Average velocity = (u + v) / 2

Therefore, Distance (t) = (u + v) / 2t       …...eq.(1)

Again from first equation of motion:

v = u + at

Substituting this value of v in eq.(1), we get

s = (u + u + at) / 2t

s = (2u + at) / 2t

s = (2ut + at²) / 2

s = (2ut / 2) + (at² / 2)

or  s = ut + (1/2) at²

This describes the second equation of motion.

Derivation of Third Equation of Motion

As it is defined that the third equation of Motion:  v² = u² + 2as

Now,

v = u + at

v – u = at

or  t = (v – u) / a            …….. eq.(2)

Also ,

Distance = average velocity x Time

Therefore, s = ((v + u) / 2) x ((v – u) / a)

s = (v² – u²) / 2a

2as = v² – u²

or  v² = u² + 2as

This describes the third equation of motion.