# Summary

- Aristotleâ€™s view that a force is necessary to keep a body in uniform motion, was actually discarded long back. A force is necessary in practice to counter the opposing force of friction.
- Galileo extrapolated general observations on motion of bodies on incident planes, and arrived at the law of inertia
**Newton's First Law of motion:**According to Newtonâ€™s first law of motion, "Every body continues to be in its state of rest or of uniform motion in a straight line, unless it is compelled by some external force. If the external force acting on the body is zero, then the acceleration also becomes zero.- The product of the mass and its velocity is called the momentum of an object.
**Newton's second law of motion:**According to Newtonâ€™s second law of motion, the rate of change of momentum of a body is proportional to the applied force and takes place in the direction in which the force acts. Thus- F= Kdp/dt =Kma
- Where F is the net external force on the body and a its acceleration. We set the constant of propornality K=1 in S.I. Then
- F= dp/dt=ma
- The S.I unit of forces is newton : 1 N = 1 Kg m s
^{2} - The second law is consistent with the first law (F = 0 implies a = 0
- It is a vector equation.
- It is applicable to a particle, and also to a body or a system of particles, provided
**F**is the total external force on the system and**a**is the acceleration of the system as a whole. **F**at a point at a certain instant determines**a**at the same point at that instant. That is the second law is a local law;**a**at an instant does not depends on the history of motion.- Impulse is the product of force and time which equals change in momentum. The notion of impulse is useful when a large force acts for a short time to produce a measurable change in momentum. Since the time of action of the force is very short, one can assume that there is no appreciable change in the position of the body during the action of the implusive force.
**Newton's third law of motion:**To every action, there is always an equal and opposite reaction- In simple term, the law can be stated thus:
- Forces in nature always occur between pairs of bodies. Force on a body A by body B is equal and opposite to the force on the body B by A.
- Action and reaction forces are simultaneous forces. There is no cause-effect relation between action and reaction. Any of the two mutual forces can be called action and other reaction. Action and reaction act on different bodies and so they can be cancelled out. The internal action and reaction force between different parts of body do, however, sum to zero.
- Laws of conservation of momentum
- The total momentum of an isolated system of particles is conserved. The law follows from second and third law of motion.
- Friction
- Frictional force opposes (impending or actual) relative motiton between two surfaces in contact. It is the component of the contact force along the common tangent to the surface in contact. Static friction fs opposes impending relative motion; Kinetic friction fk opposes actual relative motion; They are independent of the area of contact and satisfy the following approximaÎ¼te laws:

F

F

Î¼

_{s}â‰¤ (f_{s})max =Î¼_{s}RF

_{k}=Î¼_{k}RÎ¼

_{s}(co-efficient of static friction) and Î¼_{k}(co-efficient of kinetic friction) are constants characteristics of the pair of surfaces in contact. It is found experimentally that Î¼_{k}is less than Î¼_{s}.Quantity |
Symbol |
Units |
Dimensions |
Remarks |

Momentum | p | Kgms^{-1} or Ns |
[MLT^{-1}] |
Vector |

Force | F | N | [MLT^{-2}] |
F= ma Second law |

Impulse | Kgms^{-1} or Ns |
[MLT^{-1}] |
Impulse = force x time = change in momentum | |

Static friction | f_{s} |
N | [MLT^{-2}] |
f_{s} â‰¤ Î¼_{s}N |

Kinetic friction | f_{k} |
N | [MLT^{-2}] |
fk = Î¼_{k}N |