1. Momentum is the quantity of motion possessed by a body by virtue of which it can set other bodies in motion by collision.
2. Momentum is the product of mass and velocity . SI unit is kg ms-1. It is a vector having the same direction as that of velocity.
3. In finding the change in momentum, vector subtraction must be used.
4. If a ball of mass m moving with a speed v strikes a wall at right angle to it and rebounds with the same speed, then the change in momentum is 2mv.
5. If a body of mass m thrown vertically upwards with a velocity u returns to the starting point, then the change in its momentum is 2mu.
6. If a ball of mass m moving with a velocity u is struck by a bat and retraces its path with a velocity v, then the change in momentum is m(v + u).
7. Newton’s first law of motion : Every body continues to be in the state of rest or of uniform motion unless it is compelled by an external force to change that state. i.e., the momentum of a body remains constant as long as no external force acts on it.
8. The first law of motion leads to the concepts of force and inertia.
9. Inertia is the tendency of a body to preserve its state of rest or of uniform motion along a straight line in the absence of any external force
10. The three types of inertia are:
i) inertia of rest
ii) inertia of motion and
iii) Inertia of direction
11. Inertia of rest: The inability of a body to change its state of rest by itself is called inertia of rest.
Eg: When a bus at rest starts suddenly passengers fall back
12. Inertia of motion: the inability of a body to change its uniform motion by itself is called as inertia of motion.
Eg: when a bus in uniform motion suddenly stops , the passengers fall forward.
13. Inertia of direction: The inability of a body to change its direction of motion by itself is called inertia of direction.
Eg: When a bus takes a turn passengers will be pressed outwards.
14. Force is that which changes or tends to change the state of rest or of uniform motion of a body along a straight line.
15. Newton’s second law of motion : The rate of change of momentum of a body is directly proportional to the impressed force and takes place in the direction of force.
16. The second law of motion gives the direction and magnitude of force.
F = pressure × area F = mg
20. A unit force : is one which when acting on unit mass produces unit acceleration in its direction.
Units : SI unit is newton and cgs unit is dyne; 1 N = 105 dynes.
21. Gravitational unit of force :
1 kgwt = g N = 9.8 newton
1 gwt = g dynes = 980 dynes.
Force = rate of change of mass × change in velocity
F = [rocket, conveyor belt problems, etc. can be solved by this formula]
22. If a rocket ejects the exhaust gases with a velocity u relative to the rocket at the rate of , the force F acting on the rocket is F = .
23. If gravel is dropped on a conveyor belt at the rate of , the extra force required to keep the belt moving with velocity is F = .
24. A jet of water of density d from a tube of area of cross section a comes out with a velocity v.
a) Average force exerted by tube on water is dAv2
b) Force required to hold the tube in a fixed position = dAv2
c) If the water traveling horizontally strikes a vertical wall normally and then flows down along the wall, the normal force exerted on the wall is dAv2.
d) In the above case if water rebounds with the same speed, force exerted on the wall is 2dAv2
e)In the above case if water strikes the surface at angle with the normal and reflects with the same speed, force exerted on the wall is 2dAv2 Cos.
25. If a gun fires n bullets each of mass m per second each with a velocity u, the force F necessary to hold the gun is F = mnu.
26. A very large force acting for a short interval of time is called impulsive force.
Eg : Blow of a hammer on the head of a nail.
27. The impulse of a force is defined as the product of the average force and the time interval for which it acts.
29. While catching a fast moving cricket ball the hands are lowered, there by increasing the time of catch which thus decreases the force on hands.
30. A person jumping on to sand experiences less force than a person jumping on to a hard floor, because sand stops the person in more time.
31. If a force F1 acts on a body at rest for a time t1 and after that another force F2 brings it to rest again in a time t2, then F1t1 = F2t2.
32. The gravitational force that acts on a body is called its weight (W = mg). It is a vector always pointing in a vertically downward direction.
33. A bird is in a wire cage hanging from a spring balance when the bird starts flying in the cage, the reading of the balance decreases.
34. In the above case, if the bird is in a closed cage or air - tight cage and it hovers in the cage, the reading of the spring balance does not change.
35. In the above case for a closed cage if the bird accelerates upward reading of the balance is R = Wbird + ma, where m is the mass of the bird and its acceleration.
36. If a block of mass m hangs at the end of a massless string and the string is pulled up, the tension in string is T = m (g + a) if the block accelerates in the upward direction. T = m (g - a) if the block is accelerated in the downward direction. T = mg if the block is moved up or down with uniform speed.
37. When a man stands on a weighing machine, the weighing machine measures the normal force between the man and the machine.
38. When the man and the weighing machine are at rest relative to the earth, reading of the weighing machine is N = mg = Weight of the man. N is also called apparent weight.
39. Man inside an elevator:
a) Elevator accelerates up:
Same effect is felt when elevator retards while going down.
Relative to earth N-mg=ma
(M = mass of man)
Tension in the cable
T = (Melevator + Mman) (g + a)
Same effect is felt when elevator retards while going down.
b) Elevator accelerates downward:
Relative to earth mg-N=ma
Tension in the cable
T = (Melevator + Mmam) (g - a)
Same effect is felt when elevator goes up and retards.
If elevator falls freely (cable breads) N = 0
i.e. apparent weight of in a free fall = 0
40. Man inside an artificial satellite
a) An artificial satellite orbiting the earth in a circular orbit is a freely falling body because its centripetal acceleration is equal to the acceleration due to gravity in that orbit.
41. With a car at rest, mark the position of the stationary pendulum bob on the table under it, with the car in motion
a) If the bob remains over the mark only when the car is moving in a straight line at a constant speed. (inertial frame of reference)
b) If the car is gaining or losing the speed or is negotiating a bend, the bob moves from its mark and the car is a non-inertial frame.
42. If you put a ball at rest on a rotating merry-go round, no identifiable force acts on the ball but it does not remain at rest, it is non - inertial reference frame.
43. Newton’s third law : For every action there is an equal and opposite reaction.
44. Newton’s first and third laws are only special cases of second law.
45. Thrust is the total force applied on a given area. It is measured as the product of pressure and the area on which the pressure is applied.
46. In nature forces always occur in pairs (action and reaction)
47. When a body exerts a force on another body, the second body exerts a force on the first body of the same magnitude but in opposite direction.
48. If we tie one end of a string to any point of a body and pull at the other end of the string, we exert a force on the body. Such a force exerted by means of a string is called tension.
49. When two objects are connected by an inextensible massless string passing over a smooth pulley or peg, then (i) both will have the same acceleration and ii) the tension is the same on both the sides of the pulley.
52. Two masses m1 and m2 connected by a string pass over a pulley. m2 is suspended and m1 slides up over a frictionless inclined plane of angle
53. A body of mass m1 is placed on a smooth table. A string attached to m1 passes over a light pulley and carries a mass m2.
MOTION OF CONNECTED BODIES :
54. When two bodies are connected by a light string passing over a frictionless pulley
a) m1 and m2 will have the same acceleration 'a' If m2 > m1
55. A block of mass M is pulled by a rope of mass m by a force P on a smooth horizontal plane
56. Masses m1, m2, m3 are inter connected by light string and are pulled with a string with tension T3 on a smooth table.
58. Limitations of Newton’s law of motion:
a) It is applicable only for speeds
V << C (C = speed of light)
b) It is not applicable in the domain of atoms, molecules, sub atomic particles.
c) It is not applicable when there is a very strong gravitational field.
d) The concept of Newton III law is not applicable, when particles interact with each other by means of a force field
e) Newton’s laws are not applicable for very small accelerations. (a < 10–1° ms–2)