CBSE Class 11 Physics Revision Notes Chapter 5

Class 11 Physics Revision Notes for Chapter 5 – Law of Motion

Given the number of topics it contains, Physics is an essential subject for doing well on the Class 11 exams. Students should build their learning strategy not just on memorising topics but also on understanding their real-life applications. Based on the CBSE guidelines for the NCERT curriculum for Class 11, Class 11 Physics Revision Notes for Chapter 5 – Law of Motion provide the students with a way of understanding and clarifying their doubts, proving helpful for quick revisions. 

Force:

Force is basically an interaction between two bodies, which causes their state of either rest or motion to change. Physical contact is not necessary for applying force on a particular body. For example: In the case of electrostatic force or gravitational force. 

It is a vector quantity. SI unit – Newton. Dimension – [MLT-2]

Lami’s Theorem:

Let F1, F2, and F3 be three forces acting simultaneously on a body in equilibrium. 

Then, Lami’s theorem suggests that :

And ɑ, β and ? are angles opposite to the forces F1, F2 and  F3 respectively.

Basic Forces:

Four basic types of forces are :

1. Weight – The force with which a  body gets attracted towards the earth and they exert forces upon each other, like in gravitational force.
2. Contact force – Forces exerted by two bodies upon coming in contact with each other are called contact force and it is of two types, Normal force (contact force component is normal to the surface) and Frictional force (Component of contact force is parallel to surface).
3. Tension – Any strain applied to or derived from the end of a taut string, rope or chain is called tension. This force is pulling the body when in the same direction and pushing it as a default reaction. 
4. Spring force – Alteration in length leads to resistance to change its length.

Spring Force = – ?.?

Where ? = spring constant and ? = change in length. 

Newton’s Laws of Motion:

Newton’s First Law:

• An external force can only induce any change in the state of rest or motion of a body in a straight line. This is the Law of Inertia.
• Inertia refers to the property of resisting change in state by a body unless an external force acts upon it in order to bring about the change. 
• A frame of reference, whether the body is at rest or in motion, is important for this law to be valid.

Newton’s Second Law:

• The Second Law states that the rate of change of momentum of a body is directly proportional to the total resultant force acting on the body. 

F ∝ dp/dt , F ∝ ma

P = mv

dp/dt = mdv/dt

• The Change in momentum caused due to the applied resultant force, in the direction of the force applied can provide a measure of the total motion in the body. 

F = dv/dt 

Ma = P2 – P1 /t

Either the magnitude of velocity or the direction can be changed to accelerate the body in motion. 

• Special Cases :

1. A circular path will be followed if the force acts perpendicular to the motion of the body. This changes only the direction.
2. A straight-line path will be followed if the force is parallel or antiparallel to the motion, which causes a change in magnitude only. 
3. If a force acts at an angle θ, both magnitude and direction are changed, resulting in a parabolic, non-uniform circular, parabolic or hyperbolic path. 

Newton’s Third Law:

• If two forces, FA and FB, are exerted by two bodies on each other, then the force exerted by anybody will be equal to an equal and opposite force exerted by the other body. 
• FA = – FB
• An equal and opposite reaction is observed for every action. 

Linear Momentum:

Represented by P, linear momentum is the product of the mass of the body and its velocity. 

P = mV (vector)

SI unit = kg ms-1

The direction of linear momentum is the same as the direction of velocity. 

Impulse:

The average force during impact and the duration of impact, when multiplied, yields impulse.

Forces that act on bodies for a short time are impulsive forces, which vary from zero to maximum and back to zero. 

I = F av t = p2 – p1

Apparent Weight on a Body in a Lift

• a = 0 (Lift is at rest)

• mg−R=0

⇒mg=R

R=mg (1−a/g)

Wapp. =Wo (1−a/g)

R+mg−mg=0

FAB×Δt = fms = μsR

∠AOC=θ

Wapp.= Wo

• Upward movement with acceleration a

• R−mg−ma=0

⇒R=m (g+a)

⇒R=mg (1+a/g)

 ∴Wapp=Wo (1+a/g)

• Downward movement with acceleration a

• R+ma−mg=0

⇒R=mg (1−a/g)

∴Wapp=Wo (1−a/g)

• a = g (Free fall of the lift)

•  R+mg−mg=0

⇒R=0

∴Wapp=0

Principle of Conservation of Linear Momentum

As a result of Newton’s second and third law, the change in linear momentum cancels in pairs in an isolated system of individual particles. Hence, the vector sum of the entire system’s linear momenta is conserved and unaffected by their interactions with reciprocal action and response. 

An isolated system having two bodies A and B with initial linear momentum PA and PB collide and give rise to linear momenta PA’ and PB’ after the collision for a time t.

The Second Law of Newton asserts the following:

A force exerted on A by B, FAB and FBA is a force exerted on B by A :

FAB x Δt = Change in linear momentum of A = PA’ – PB’

FBA x Δt = Change in linear momentum of B= PB’ –  PA’ 

The third law of motion asserts :

FAB = -FBA

Thus, PA’ – PA’  =  PB’ – PB’ 

Or  PA’ + PB’ = PA’ + PB’

Total final linear momentum = Total initial linear momentum

Friction:

Two surfaces in contact oppose each other’s motion, due to the force of friction. 

1. Friction is unaffected by the contact area. As the area increases, adhesion between surfaces increases.
2. Extra smooth surfaces have a higher force of friction, since molecules of the surface have larger distances between them, increasing the adhesion. 

Types of Friction:

• Static friction: When a body moves over another body but action motion has not occurred

• Limiting Friction: One body is just about to move on another, and a maximum opposing force comes into play.

• Kinetic Friction: Actual movement of one body on the surface of another body leads to friction. 

Laws of Limiting Friction:

1. Friction works in the opposite direction of motion and thus is a reverse force.
2. Limiting friction is proportional to the normal reaction (R)  [fms ∝ R]
3. Limiting friction is expressed as a tangent to the interface between the two surfaces in contact
4. The limiting friction is independent of the area of the surfaces in contact if R is constant. 

Coefficient of Static Friction:

• We know, 

fms ∝ R

fms =  μsR

Where, μs is the coefficient of static friction. 

The value of μs ranges from zero to maximum (fs fms)

• The force of kinetic friction fk is directly proportional to the normal reaction, fk ∝ R ⇒  fk = μkR

• Rolling friction occurs when a body rolls over the surface of another body. 

Angle of Friction (θ)

The angle formed by the resultant of the limiting friction force F and the normal reaction R. 

Determination of the angle of friction can be done by noting the material of the surfaces in contact and the nature of the surfaces themselves.

Angle of Repose or Angle of Sliding:

Represented by α, the angle of sliding is the minimum angle of inclination of a plane with the horizontal at which the body begins to slide. It depends on the material and nature of surfaces in contact.

Forces involved in α :

• Weight (mg) resolved into two components – mg sin α (opposite to F) and mg cos α (opposite to R )
• Normal reaction (R )
• Frictional force (F)

Dividing F by R, 

tan α = mg sin α / mg cos α  = μ = tan θ ; α = θ

Methods of Changing Friction:   

Methods of reducing friction are :

• Polishing
• Lubrication
• Selection of correct material
• Streamlining
• Using ball bearings 

Dynamics of Uniform Circular Motion Concept of Centripetal Force:

The external force needed to shift a body’s motion along a circular path is known as centripetal force. This force is applied tangentially. Centripetal acceleration refers to a change in velocity that occurs during this motion. 

F=mv2/ r=mω2r

 R − mg = 0 or R = mg

F = μs R = μs mg 

R cosθ= mg + F sinθ

⇒ R (cosθ − μs sinθ) = mg

Centrifugal Force:

A body moving in a straight path moves in a circle, and shows an inclination to return to its straight path, which leads to centrifugal force. 

Fcf = mv2 / r; in the opposite direction to centripetal force, away from the centre. 

Rounding A-Level Curved Road:

A centripetal force is needed when a vehicle moves on a curved road. The wheels tend to their straight line path during the curve when a force of friction opposes this tendency. Slipping can be avoided by using this concept, 

The maximum velocity with which a car can move without slipping is 

V = √μsrg

Banking of Roads:

Banking of roads refers to raising the outer edge of the curved road to prevent vehicles from skidding. There exists a permitted range of velocity, which depends on μ (coefficient of friction between the tyre and road). 

Factors acting on the vehicle in this case are :

1. Weight (mg)
2. Normal reaction (R )
3. Force of friction F

• R cos θ, vertically upwards
• R sin θ, along the horizontal
• F  cos θ, along the horizontal, towards the centre
• F  sin θ, along the vertical, away from the centre

R cosθ= mg + F sinθ       …… (1)

Rsinθ + Fcosθ=mv2r       …….(2)

F = μsR  in (1) and (2)

R cos θ = mg + μsR sinθ ……(3)

Rsinθ + μsRcosθ = mv2/ r ……(4) 

From (3), 

R (cosθ−− μssinθ) = mg 

R= mg / cosθ−μssinθ….…(5)

From (4), 

R (sinθ+μscosθ) = mv2 / r

Using (5)

Mg (sinθ+μscosθ) / (cosθ−μssinθ)= mv2 / r

∴v2 =rg (sinθ+μscosθ)/(cosθ−μssinθ)= rgcosθ(tanθ+μs) / cosθ(1−μstanθ)

v= [rg(μs+tanθ) / (1−μstanθ)]1/2      ………(6) 

Discussion:

• If the banked road is perfectly smooth, and μs = 0, then in absence of friction, the speed at which a banked road is rounded is given as 

• Vo = (rg tan θ)½  or vo2 = rg tan θ
• Freal + Fpseudo = mpaP,O
• Freal –  mpa0 = mpaP,O

• Self-adjusting static friction develops between the tyres if the vehicle’s speed is slightly less or more than the average speed of vehicles passing. 

If speed is less than Vo, the frictional force is up the slope, parking will occur only if tan θ μs

Bending of a Cyclist:

The centripetal force applied by a cyclist during a turn, as the ground’s normal reaction, balances the weight of the cyclist. Friction generates this necessary centripetal force between the road and the tyre. However, this force of friction is dangerous, therefore the rider can generate the necessary centripetal force by bending slightly inward from a vertical posture.

If the cyclist’s weight (mg) acts at the centre of gravity (C) in a vertically downward direction and the normal reaction (R) acts on the cyclist at an angle of, then R can be divided into two rectangular components, R cos (along the vertically upward direction) and R sin (along the horizontal downward direction) (along the horizontal)

In equilibrium, R cos θ = mgR cos θ = mg  ……….(1)

And,                   R sin θ = mv2 / r                   ………..(2)

Dividing (2) by (1) 

Tan θ = v2 / rg 

If θ is small, then v should be small, and r should ideally be large. Thus, the turn should be taken on a wider radius, in slow speed. 

Here, Thus,

M = mass of cyclist

V = velocity of the cyclist while turning

R = radius of circular path 

Θ = angle of bending w the vertical. 

Pseudo Force:

A pseudo force is added when an observer O is non-inertial and wishes to use Newton’s Second Law on a particle P. 

Fpseudo  =   – mpaO

Freal + Fpseudo = mpaP,O

Thus, Freal – mpa0 = mpaP, O

aP, O is the acceleration of P with respect to observer O.

Laws of Motion Class 11 Notes – Free Download

The concise format of the revision notes for students of Class 11 allows for a quicker grasp of concepts in a lesser time. Students may refer to these notes to clear any last-minute doubts as subject matter experts produce these notes. They need not fret by referring to multiple sources due to the authenticity and dependability of these notes. It boosts the confidence of every student before their final examinations. An easy-to-access option allows students the flexibility to study according to their schedules. 

What Topics are Covered With Ch 5 Physics Class 11 Notes?

An effective presentation of concepts from ​​Class 11 Physics Chapter 5, Revision Notes from Extramarks provide the following details :

• Understanding of the branch Dynamics, studying forces and concept of motion.
• The concept of friction is explored along with the concept of inertia.
• Many numerical problems come from this chapter, since it has many concepts that require mathematical calculations. 

Dynamics 

The branch of physics dealing with the understanding of motion, laws of motion and forces is called Dynamics. 

Inertia

Inertia is the property of a body to not change its state unless made to do so. Mass of the body helps in measurement of inertia. Three types of inertia are:

• Inertia of motion
• Inertia of rest
• Inertia of direction

Force 

When objects interact with each other, they experience a basic ‘push’ or ‘pull’ applied to them. This is the force, due to which an object may or may not change its state. The two types of forces are: Constant Force and Action force. 

Newton’s Laws of Motion

The three laws of motion given by Newton include:

• First Law: The Law of Inertia, given by Newton as the First Law of Motion, states that unless an external force is applied to an object, it remains in a uniform state of rest or uniform state of motion. 
• Second Law: The Second Law of Motion states that the net force is equivalent to both the magnitude and direction of the applied force. Force is directly proportional to acceleration and mass of the body. 

F=Kma

where F = net force, m = mass of the body, a = acceleration and k = constant of proportionality. 

• Third Law: If a force is applied to an object, the object will apply an equal and opposite force in return.

This Law Deals With Some Other Basic Subtopics 

Many concepts are covered in Class 11 Physics Revision Notes Chapter 5, some of which are Linear Momentum, Impulse, Law of Conservation of momentum, Concurrent forces and Equilibrium. Other concepts like Tension, Angle of Friction, Motion in a circle, etc, are also explained in this chapter. 

Why Should You Choose Extramarks for Class 11 Chapter 5 Physics Notes?

The Extramarks Class 11 Physics Revision Notes for Chapter 5 provide a detailed overview of each concept in the chapter in simple terms. Students can plan flexible study schedules and effectively finish the syllabus well in time for revision with the help of these notes to avoid any last-minute exam stress. Subject matter experts create content that covers all concepts in an easy-to-comprehend manner. 

Below Are the Points Which State Why Should Students Prefer Having Class 11 Physics Chapter 5 Notes

• The notes are created by subject matter experts, which makes them precise and reliable. 
• Topics are written in an easy-to-comprehend manner, enabling efficient revisions in lesser time. 
• Saves the effort to refer to multiple sources immediately and avoids confusion.

Conclusion

A transition from the method of study for numerous students from Class 10 to Class 11 could be stressful for many reasons. The NCERT curriculum for Class 11 focuses on conceptualising the basics of every subject learnt up to Class 10, enabling students to grasp the subject more efficiently. With the assistance of quality notes and study materials, students will be better able to make the transition. Extramarks offers Class 11 Physics Revision Notes for Chapter 5 that help students learn ‘Laws of Motion’ for all-rounded exam preparation.