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Laws of Motion & Friction Class 11 Notes Physics

MOMENTUM
Momentum of a particle (p) is equal to the mass of the particle (m) times velocity of the particle (v). So, p = mv

Laws of Motion & Friction Class 11 Notes Physics

Question for Revision Notes: Laws of Motion & Friction
Try yourself:Two trains A and B are running in the same direction on parallel tracks such that A is faster than B. If packets of equal weight are exchanged between the two, then
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NEWTON LAWS OF MOTION
(i) First Law (Law of Inertia): Everybody continues in its state of rest or of uniform motion in a straight line unless it is compelled by some external force to change that state.
(ii) Second Law: The rate of change of momentum of a body is directly proportional to the impressed force and takes place in the direction of the force.
So, F = dp/dt
This results force acting a body F is equal to the mass of the body m times acceleration of the body a.
So, F = ma
(iii) Third Law: To Every action there is an equal and opposite reaction.
FAB = - FBA 

  • Impulse: Impulse of a force is defined as the change in momentum produced by the force and it is equal to the product of force and the time for which it acts.
    Laws of Motion & Friction Class 11 Notes Physics

So,  J = Ft
= mv – mu

  • Apparent weight of a man inside a lift:

Laws of Motion & Friction Class 11 Notes Physics
(a) The lift possesses zero acceleration (fig-1): W = m
(b) The lift moving upward with an acceleration a (fig-2):
W = mg + ma
W= mg + mg
W= 2 mg
(c) The lift moving downward with an acceleration a (fig-3):
W = mg – ma
W = mg – mg
W = 0

  • Inertial mass (mi)- It is defined as the ratio between force F to the acceleration a a produced in the body.
    So, mi = F/a

NOTE 
When the velocity of a body is comparable to the velocity of light, inertial mass changes with velocity in accordance with following formula,
mi = mi0/√(1-v2/c2)
Here mi0 is the rest mass of body, v is the velocity of body and c is the velocity of light.

  • Conservation of linear momentum:
    In an isolated system (no external force), the algebraic sum of the momentum of bodies, along any straight line, remains Laws of Motion & Friction Class 11 Notes Physics constant and is not changed due to their mutual action and reaction on each other.
  • Recoil of gun: If m is the mass of the bullet, M is the mass of gun and v is the mass of the bullet, then, velocity of the recoil of gun  V will be, 
  • Equilibrium of concurrent forces: 
    Forces are said to be concurrent if they meet at a common point. Below figure shows three concurrent forces ,  Laws of Motion & Friction Class 11 Notes Physics
     Laws of Motion & Friction Class 11 Notes Physics
  • Moment of the force = F×d
    Here F is the force and d is the distance of line of action.
  • Momentum of a couple (Torque (τ)): Momentum of a couple is equal to the product of force F and the perpendicular distance r between them. Laws of Motion & Friction Class 11 Notes Physics
  • Work done by a couple: (W)
    W = τ × θ
    Here θ is the angular displacement.


  • Connected Motion (Pulley Problem)
    (a) Driven body moving vertically: 
    Acceleration of the system, a = (M-m/M+m) g  
    Tension in the string, T = (2Mm/M+m) g
    The force on the pulley, F = (4Mm/M+m) g

Laws of Motion & Friction Class 11 Notes Physics(b) Driven body moving horizontally:
Acceleration of the system, a = (M /M+m) g
Tension in the string, T= (Mm/M+m) g
The force on the pulley, F= [√2 (Mm) /M+m] g
Here g is the free fall acceleration.
Laws of Motion & Friction Class 11 Notes Physics

  • Application of Newton’s third law on contact of two block:
    (a) Acceleration, a =F/(m + M)
    (b) Laws of Motion & Friction Class 11 Notes Physics
    (c) Contact force, F12 = (m/m+M) F = F21
    Laws of Motion & Friction Class 11 Notes Physics
  • Friction: Whenever a body tends to slide over another’s surface, an opposing force, called force of friction comes into play. This force acts tangentially to the interface of two bodies.
  • Static friction: Static friction is the force of friction between two surfaces so long as there is no relative motion between them. It is always equal to the applied force. The static frictional forces are incorporated in the following inequality.
    fs  ≤ µsN
  • The magnitude of static friction fs (static frictional force) has a maximum value fs,max that is given by,
    fs,max  = µsN
    Here µs is the coefficient of kinetic friction and N is the normal force.
    So, coefficient of static friction, µs = fs,max /N
  • Kinetic friction: Kinetic friction is the force of friction which comes into play between two surfaces when there is some relative motion between them. The magnitude of force of kinetic friction f(kinetic frictional force) is proportional to the normal force N.
    So, fk = µk N
    Here µk is the coefficient of kinetic friction.
    Thus, coefficient of kinetic friction, µk = fk/N  
  • µk < µs
  • Rolling friction: Force of friction which comes into play, between two surfaces, while one is rolling over the other is called rolling friction.  Rolling friction is similar to kinetic friction.
    So, f= µN
    Here µr is the coefficient of rolling friction and N is the normal force.
Question for Revision Notes: Laws of Motion & Friction
Try yourself:Maximum value of frictional force is called
View Solution
  • Angle of Friction:
    The angle made by the resultant reaction force with the vertical (normal reaction) is known as the angle of the friction.
    Now,  in the triangle OAB
    AB/OB = cotθ
    So, OB = AB/cotθ
    = AB tanθ
    Or, tanθ = OB/AB
    = f/N
    So, tanθ = f/N  = µs
    Laws of Motion & Friction Class 11 Notes Physics
  • Angle of Repose: It is the angle which an inclined plane makes with the horizontal so that a body placed over it just begins to slide of its own accord.
    Consider a body of mass m resting on an inclined plane of inclinationq. The forces acting on the body are shown – Ff being the force of friction. If friction is large enough, the body will not slide down.
    along x: mg sin θ – f = 0             …(1)
    Along y: N –mg cosθ = 0                …(2)
    i.e. N = mg cos θ and f = mg sin θ
    Thus,  gives, Laws of Motion & Friction Class 11 Notes Physics
    mg sin θ ≤  μS mg cos θ
    Laws of Motion & Friction Class 11 Notes Physics
    So,  tan θ ≤ μS. This signifies, the coefficient of static friction between the two surfaces, in order that the body doesn’t slide down.
    When q is increased, then tan θ > μ. Thus sliding begins, and the angle θr  = tan-1μ. This angle is known as the angle of repose.
  • Acceleration on a horizontal plane: a = (F - µkN)/m   
  • If Laws of Motion & Friction Class 11 Notes Physicsbe the acceleration of frame, the pseudo force will be,
    Laws of Motion & Friction Class 11 Notes Physics(Example: centrifugal force = mv2/r = mrω2)
  • Gravitational mass (mg):
    mg = F /g
    = FG r2/GM
    Here, g is the free fall acceleration, FG is the gravitational force and G is the gravitational constant.
The document Laws of Motion & Friction Class 11 Notes Physics is a part of the NEET Course NCERT Exemplar & Revision Notes for NEET.
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FAQs on Laws of Motion & Friction Class 11 Notes Physics

1. What are Newton's laws of motion?
Ans. Newton's laws of motion are three fundamental principles that describe the relationship between the motion of an object and the forces acting on it. The laws are: 1) The law of inertia, which states that an object at rest will stay at rest and an object in motion will stay in motion with the same speed and in the same direction unless acted upon by an external force. 2) The law of acceleration, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. 3) The law of action and reaction, which states that for every action, there is an equal and opposite reaction.
2. How does friction affect motion?
Ans. Friction is a force that opposes the motion of objects in contact with each other. It acts in the opposite direction of the object's motion. Friction can either increase or decrease the speed of an object, depending on the direction of the force. For example, when you push a book on a table, the force of friction between the book and the table slows down the book's motion. On the other hand, friction between the tires of a car and the road helps the car to stop or change direction.
3. What factors affect the amount of friction between two surfaces?
Ans. The amount of friction between two surfaces depends on several factors, including the nature of the surfaces, the force pressing the surfaces together, and the presence of any lubricants. Rougher surfaces tend to have more friction than smoother surfaces. The force pressing the surfaces together, also known as the normal force, affects the amount of friction. The greater the normal force, the greater the friction. Lubricants, such as oil or grease, can reduce friction by creating a slippery barrier between the surfaces.
4. How does Newton's first law of motion relate to the concept of inertia?
Ans. Newton's first law of motion, also known as the law of inertia, states that an object at rest will stay at rest and an object in motion will stay in motion with the same speed and in the same direction unless acted upon by an external force. Inertia is the tendency of an object to resist changes in its state of motion. According to Newton's first law, an object at rest will remain at rest because it has inertia and resists any changes in its motion. Similarly, an object in motion will continue moving in a straight line at a constant speed because of its inertia.
5. How does Newton's third law of motion explain the motion of objects in contact?
Ans. Newton's third law of motion states that for every action, there is an equal and opposite reaction. This means that when two objects interact, they exert equal and opposite forces on each other. In the context of objects in contact, this law explains how forces are exchanged between the objects. For example, when you push a wall, you exert a force on the wall, and the wall exerts an equal and opposite force on you. This force pair allows the wall to resist your push and prevents you from moving through it.
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