Newton's Law of Motion | Physics Optional Notes for UPSC PDF Download

 Page 1


Newton's Laws of Motion 
Three fundamental quantities are : 
(i) Mass, 
(ii) Motion & 
(iii) Force 
Mass 
The amount of matter in something is determined by its density and size together. 
Motion 
The quantity of motion is the measure of the same arising from the velocity and quantity 
of matter conjointly. 
Force  
 
The vis-insita, or an object's innate force, is its natural ability to resist changes to its 
current condition. This means that any object will try its best to stay as it is, whether 
that's staying still or moving straight ahead at a constant speed. 
 (OR) 
An impressed force is an action exerted upon a body, in order to change its state, either 
of rest, or of moving uniformly forward in a right line. 
These definitions gave rise to the famous three laws: known as Newton's laws of motion. 
Law 1 
Everybody continues in its state of rest or of uniform rectilinear motion except if it is 
compelled by forces acting on it to change that state. 
Law 2 
The change of motion is proportional to the applied force and takes place in the direction 
of the straight line along which that force acts. 
Laws 3 
To every action there is always an equal and contrary reaction, or the mutual actions of 
any two bodies are always equal and oppositely directed along the same straight line. 
Page 2


Newton's Laws of Motion 
Three fundamental quantities are : 
(i) Mass, 
(ii) Motion & 
(iii) Force 
Mass 
The amount of matter in something is determined by its density and size together. 
Motion 
The quantity of motion is the measure of the same arising from the velocity and quantity 
of matter conjointly. 
Force  
 
The vis-insita, or an object's innate force, is its natural ability to resist changes to its 
current condition. This means that any object will try its best to stay as it is, whether 
that's staying still or moving straight ahead at a constant speed. 
 (OR) 
An impressed force is an action exerted upon a body, in order to change its state, either 
of rest, or of moving uniformly forward in a right line. 
These definitions gave rise to the famous three laws: known as Newton's laws of motion. 
Law 1 
Everybody continues in its state of rest or of uniform rectilinear motion except if it is 
compelled by forces acting on it to change that state. 
Law 2 
The change of motion is proportional to the applied force and takes place in the direction 
of the straight line along which that force acts. 
Laws 3 
To every action there is always an equal and contrary reaction, or the mutual actions of 
any two bodies are always equal and oppositely directed along the same straight line. 
By solving Newton's laws we shall find ?? (?? ). ?? (?? ) = 0: implies that the body is at rest for 
all time. In general, 
?? (?? ) = (?? (?? ), ?? (?? ), ?? (?? )) or (?? (?? ), ?? (?? ), ?? (?? )) 
Example 
?? (?? ) = (?? ?? ?? + ?? 0
; 0; ?? ?? ?? + ?? 0
- ?? ?? 2
/2) 
Represents uniform motion in the ?? -direction with ?? ?? as the velocity, in a state of rest in 
the ?? -direction and has a uniform velocity ?? ?? and a free fall in the gravitational field. 
Mechanics of particles 
 
Newton's First Law of Motion 
1. Defines (zero) force 
 2. Defines an inertial frame. 
Zero Force: If an object is moving in a straight line at a steady speed, it means no 
forces are acting on it, or all the forces balance out to zero ( ?F = 0). If the object starts to 
speed up, slow down, or change direction, it's because there's an unbalanced force acting 
on it, causing it to accelerate. Changes in velocity can happen because of changes in 
speed, direction, or both. 
Inertial Frame: When two reference frames move at a steady speed relative to each 
other, meaning their relative acceleration is zero (A = dV/dt = 0), they are called inertial 
reference frames. An inertial frame is a viewpoint where Newton's first law of motion 
applies without any complications. 
Page 3


Newton's Laws of Motion 
Three fundamental quantities are : 
(i) Mass, 
(ii) Motion & 
(iii) Force 
Mass 
The amount of matter in something is determined by its density and size together. 
Motion 
The quantity of motion is the measure of the same arising from the velocity and quantity 
of matter conjointly. 
Force  
 
The vis-insita, or an object's innate force, is its natural ability to resist changes to its 
current condition. This means that any object will try its best to stay as it is, whether 
that's staying still or moving straight ahead at a constant speed. 
 (OR) 
An impressed force is an action exerted upon a body, in order to change its state, either 
of rest, or of moving uniformly forward in a right line. 
These definitions gave rise to the famous three laws: known as Newton's laws of motion. 
Law 1 
Everybody continues in its state of rest or of uniform rectilinear motion except if it is 
compelled by forces acting on it to change that state. 
Law 2 
The change of motion is proportional to the applied force and takes place in the direction 
of the straight line along which that force acts. 
Laws 3 
To every action there is always an equal and contrary reaction, or the mutual actions of 
any two bodies are always equal and oppositely directed along the same straight line. 
By solving Newton's laws we shall find ?? (?? ). ?? (?? ) = 0: implies that the body is at rest for 
all time. In general, 
?? (?? ) = (?? (?? ), ?? (?? ), ?? (?? )) or (?? (?? ), ?? (?? ), ?? (?? )) 
Example 
?? (?? ) = (?? ?? ?? + ?? 0
; 0; ?? ?? ?? + ?? 0
- ?? ?? 2
/2) 
Represents uniform motion in the ?? -direction with ?? ?? as the velocity, in a state of rest in 
the ?? -direction and has a uniform velocity ?? ?? and a free fall in the gravitational field. 
Mechanics of particles 
 
Newton's First Law of Motion 
1. Defines (zero) force 
 2. Defines an inertial frame. 
Zero Force: If an object is moving in a straight line at a steady speed, it means no 
forces are acting on it, or all the forces balance out to zero ( ?F = 0). If the object starts to 
speed up, slow down, or change direction, it's because there's an unbalanced force acting 
on it, causing it to accelerate. Changes in velocity can happen because of changes in 
speed, direction, or both. 
Inertial Frame: When two reference frames move at a steady speed relative to each 
other, meaning their relative acceleration is zero (A = dV/dt = 0), they are called inertial 
reference frames. An inertial frame is a viewpoint where Newton's first law of motion 
applies without any complications. 
 
?? ?
'
= ?? ? - ?? ??? , ?? ? =
?? ?? ? ?
????
 
Galilean transformation 
Is Earth an Inertial frame? 
The first law does not hold in an arbitrary frame. For example, it fails in the frame of a 
rotating turntable. 
Newton's Second Law of Motion: 
If a force causes a change in motion, then applying that force will result in twice the 
change in motion, and three times the force will lead to three times the change in 
motion. This is true regardless of whether the force is applied all at once or gradually 
over time. 
Change of motion is described by the change in momentum of the body. For a point mass 
particle, the momentum is defined as ?? ? = ?? ?? ? 
Suppose that a force is applied to a body for a time interval??? . The impressed force or 
impulse produces a change in the momentum of the body, 
?? ?
¯
= ?? ?
¯
??? = ???? ? ? 
The instantaneous action of the total force acting on a body at a time ?? is defined by 
taking the mathematical limit as the time interval ??? becomes smaller and smaller, 
 
Page 4


Newton's Laws of Motion 
Three fundamental quantities are : 
(i) Mass, 
(ii) Motion & 
(iii) Force 
Mass 
The amount of matter in something is determined by its density and size together. 
Motion 
The quantity of motion is the measure of the same arising from the velocity and quantity 
of matter conjointly. 
Force  
 
The vis-insita, or an object's innate force, is its natural ability to resist changes to its 
current condition. This means that any object will try its best to stay as it is, whether 
that's staying still or moving straight ahead at a constant speed. 
 (OR) 
An impressed force is an action exerted upon a body, in order to change its state, either 
of rest, or of moving uniformly forward in a right line. 
These definitions gave rise to the famous three laws: known as Newton's laws of motion. 
Law 1 
Everybody continues in its state of rest or of uniform rectilinear motion except if it is 
compelled by forces acting on it to change that state. 
Law 2 
The change of motion is proportional to the applied force and takes place in the direction 
of the straight line along which that force acts. 
Laws 3 
To every action there is always an equal and contrary reaction, or the mutual actions of 
any two bodies are always equal and oppositely directed along the same straight line. 
By solving Newton's laws we shall find ?? (?? ). ?? (?? ) = 0: implies that the body is at rest for 
all time. In general, 
?? (?? ) = (?? (?? ), ?? (?? ), ?? (?? )) or (?? (?? ), ?? (?? ), ?? (?? )) 
Example 
?? (?? ) = (?? ?? ?? + ?? 0
; 0; ?? ?? ?? + ?? 0
- ?? ?? 2
/2) 
Represents uniform motion in the ?? -direction with ?? ?? as the velocity, in a state of rest in 
the ?? -direction and has a uniform velocity ?? ?? and a free fall in the gravitational field. 
Mechanics of particles 
 
Newton's First Law of Motion 
1. Defines (zero) force 
 2. Defines an inertial frame. 
Zero Force: If an object is moving in a straight line at a steady speed, it means no 
forces are acting on it, or all the forces balance out to zero ( ?F = 0). If the object starts to 
speed up, slow down, or change direction, it's because there's an unbalanced force acting 
on it, causing it to accelerate. Changes in velocity can happen because of changes in 
speed, direction, or both. 
Inertial Frame: When two reference frames move at a steady speed relative to each 
other, meaning their relative acceleration is zero (A = dV/dt = 0), they are called inertial 
reference frames. An inertial frame is a viewpoint where Newton's first law of motion 
applies without any complications. 
 
?? ?
'
= ?? ? - ?? ??? , ?? ? =
?? ?? ? ?
????
 
Galilean transformation 
Is Earth an Inertial frame? 
The first law does not hold in an arbitrary frame. For example, it fails in the frame of a 
rotating turntable. 
Newton's Second Law of Motion: 
If a force causes a change in motion, then applying that force will result in twice the 
change in motion, and three times the force will lead to three times the change in 
motion. This is true regardless of whether the force is applied all at once or gradually 
over time. 
Change of motion is described by the change in momentum of the body. For a point mass 
particle, the momentum is defined as ?? ? = ?? ?? ? 
Suppose that a force is applied to a body for a time interval??? . The impressed force or 
impulse produces a change in the momentum of the body, 
?? ?
¯
= ?? ?
¯
??? = ???? ? ? 
The instantaneous action of the total force acting on a body at a time ?? is defined by 
taking the mathematical limit as the time interval ??? becomes smaller and smaller, 
 
Newton's Third Law of Motion: 
Think about two objects that are interacting with each other, calling them object 1 and 
object 2. The force that object 1 experiences because of its interaction with object 2 is 
represented as F 1, 2, and the force felt by object 2 as a result of its interaction with object 1 
is shown as F 2, 1. 
 (1) ? ?? ?
1,2
 ?? ?
2,1
? (2) ?? ?
1,2
= -?? ?
2,1
 
Gravitational force:                     ?? ?
12
= -?? ?? 1
?? 2
?? 2
?? ˆ
12
 ?? ˆ
12
= -?? ˆ
21
 
Coulomb force:                             ?? ?
12
= ?? ?? 1
?? 2
?? 2
?? ˆ
12
 ?? ?
12
= -?? ?
21
 
All real Forces arise due to interaction! 
If a body speeds up or slows down because of a force from outside, somewhere else in the 
universe, there's another body experiencing a force in the opposite direction. Even if the 
interaction seems complex, as long as these forces are equal and opposite, Newton's laws 
are followed. 
Newton's 3
rd 
 Law emphasizes the Conservation of 
Momentum 
Validity of Newton's laws 
? Validity of the first two laws 
? The first law is always valid (add a pseudo force). 
? The second law F = ?? ? holds but F and ?? have different expressions in the 
relativistic limit. 
? The 3
rd 
 law is not valid in the relativistic limit. Why???? 
Consider two positive charges 
 
Page 5


Newton's Laws of Motion 
Three fundamental quantities are : 
(i) Mass, 
(ii) Motion & 
(iii) Force 
Mass 
The amount of matter in something is determined by its density and size together. 
Motion 
The quantity of motion is the measure of the same arising from the velocity and quantity 
of matter conjointly. 
Force  
 
The vis-insita, or an object's innate force, is its natural ability to resist changes to its 
current condition. This means that any object will try its best to stay as it is, whether 
that's staying still or moving straight ahead at a constant speed. 
 (OR) 
An impressed force is an action exerted upon a body, in order to change its state, either 
of rest, or of moving uniformly forward in a right line. 
These definitions gave rise to the famous three laws: known as Newton's laws of motion. 
Law 1 
Everybody continues in its state of rest or of uniform rectilinear motion except if it is 
compelled by forces acting on it to change that state. 
Law 2 
The change of motion is proportional to the applied force and takes place in the direction 
of the straight line along which that force acts. 
Laws 3 
To every action there is always an equal and contrary reaction, or the mutual actions of 
any two bodies are always equal and oppositely directed along the same straight line. 
By solving Newton's laws we shall find ?? (?? ). ?? (?? ) = 0: implies that the body is at rest for 
all time. In general, 
?? (?? ) = (?? (?? ), ?? (?? ), ?? (?? )) or (?? (?? ), ?? (?? ), ?? (?? )) 
Example 
?? (?? ) = (?? ?? ?? + ?? 0
; 0; ?? ?? ?? + ?? 0
- ?? ?? 2
/2) 
Represents uniform motion in the ?? -direction with ?? ?? as the velocity, in a state of rest in 
the ?? -direction and has a uniform velocity ?? ?? and a free fall in the gravitational field. 
Mechanics of particles 
 
Newton's First Law of Motion 
1. Defines (zero) force 
 2. Defines an inertial frame. 
Zero Force: If an object is moving in a straight line at a steady speed, it means no 
forces are acting on it, or all the forces balance out to zero ( ?F = 0). If the object starts to 
speed up, slow down, or change direction, it's because there's an unbalanced force acting 
on it, causing it to accelerate. Changes in velocity can happen because of changes in 
speed, direction, or both. 
Inertial Frame: When two reference frames move at a steady speed relative to each 
other, meaning their relative acceleration is zero (A = dV/dt = 0), they are called inertial 
reference frames. An inertial frame is a viewpoint where Newton's first law of motion 
applies without any complications. 
 
?? ?
'
= ?? ? - ?? ??? , ?? ? =
?? ?? ? ?
????
 
Galilean transformation 
Is Earth an Inertial frame? 
The first law does not hold in an arbitrary frame. For example, it fails in the frame of a 
rotating turntable. 
Newton's Second Law of Motion: 
If a force causes a change in motion, then applying that force will result in twice the 
change in motion, and three times the force will lead to three times the change in 
motion. This is true regardless of whether the force is applied all at once or gradually 
over time. 
Change of motion is described by the change in momentum of the body. For a point mass 
particle, the momentum is defined as ?? ? = ?? ?? ? 
Suppose that a force is applied to a body for a time interval??? . The impressed force or 
impulse produces a change in the momentum of the body, 
?? ?
¯
= ?? ?
¯
??? = ???? ? ? 
The instantaneous action of the total force acting on a body at a time ?? is defined by 
taking the mathematical limit as the time interval ??? becomes smaller and smaller, 
 
Newton's Third Law of Motion: 
Think about two objects that are interacting with each other, calling them object 1 and 
object 2. The force that object 1 experiences because of its interaction with object 2 is 
represented as F 1, 2, and the force felt by object 2 as a result of its interaction with object 1 
is shown as F 2, 1. 
 (1) ? ?? ?
1,2
 ?? ?
2,1
? (2) ?? ?
1,2
= -?? ?
2,1
 
Gravitational force:                     ?? ?
12
= -?? ?? 1
?? 2
?? 2
?? ˆ
12
 ?? ˆ
12
= -?? ˆ
21
 
Coulomb force:                             ?? ?
12
= ?? ?? 1
?? 2
?? 2
?? ˆ
12
 ?? ?
12
= -?? ?
21
 
All real Forces arise due to interaction! 
If a body speeds up or slows down because of a force from outside, somewhere else in the 
universe, there's another body experiencing a force in the opposite direction. Even if the 
interaction seems complex, as long as these forces are equal and opposite, Newton's laws 
are followed. 
Newton's 3
rd 
 Law emphasizes the Conservation of 
Momentum 
Validity of Newton's laws 
? Validity of the first two laws 
? The first law is always valid (add a pseudo force). 
? The second law F = ?? ? holds but F and ?? have different expressions in the 
relativistic limit. 
? The 3
rd 
 law is not valid in the relativistic limit. Why???? 
Consider two positive charges 
 
Each of the positive charges ?? 1
 and ?? 2
 produces a magnetic field that exerts a force on the 
other charge. The resulting magnetic forces ?? 12
 and ?? 21
 do not obey Newton's third law. 
{ Note: Momentum conservation is not valid} 
Application of Newton's Laws: Prescription 
Step 1: Divide a composite system into constituent systems each of which can be treated 
as a point mass. 
Step 2: Draw free body force diagrams for each point mass. 
Step 3: Introduce a coordinate system, the inertial frame, and write the equations of 
motion. 
Step 4: The motion of a body may be constrained to move along a certain path or plane. 
Express each constraint by an equation called constraint equation. 
Step 6: Identify the number of unknown quantities. There must be enough equations 
(Equations of motion + constraint equations) to solve for all the unknown quantities. 
Example 1 
A 4Kg block rests on top of a 6Kg block, which rests on a frictionless table. Coefficient of 
friction between blocks is 0.25 . A force ?? = 10 N is applied to the lower block. 
 
Identify the constraints 
Fix the coordinate system to the table.