Motion And Its Laws

 Newton proposed three laws of motion:

i. Newton's first law of motion:
Everybody in the universe will remain in the state of rest or of uniform motion in a straight line unless no external force act on it. It gives the defination of force as "force is that external agent which changes or tends to change the state of rest or of uniform motion in a straight line".
Inertia is the tendency of a body to remain in its own state unless external force act on it. It is divided as:
a) Inertia of rest
b) Inertia of motion and
c) Inertia of direction
     Hence, Newton's first law of motion is also called Law of inertia.

 Momentum (P):
 The quantity of motion contained by a body which is equal to the product of mass and velocity is known as momentum.
   Therefore, Momentum(P) = m * v
  It is a Vector quantity.

ii. Newton's second law of motion:
It states that "the rate of change in momentum of a body is directly proportional to the force act on a body and displacement takes place in the direction of force".
    Therefore, force (F) = dp/dt
                                    = d(mv)/dt
                                    = mdv/dt + vdm/dt
    If m is constant then, F = ma
    If v is constant then, F = vdm/dt

iii. Newton's third law of motion:
It states that "for every action there is equal and opposite reaction". Action and reaction act on two different bodies so they never cancel eachother.

2. Impulse:
 The net effect of force acting on a body is measured by a quantity called impulse.
Hence, impulse (I) = P2 - P1 = Change in momentum.

3. Motion in a lift:
  When a person of mass (m) is standing on the floor of lift at rest R = mg is called weight of a person. For uniform motion of a lift a = 0 so,
 Net force = R - mg = ma
or, R - mg = 0
or, R = mg

 i. When lift is accelerating upward:
 When lift is accelerating upward with an acceleration (a) then,
R - mg = ma
or, R = mg+ma

 Reaction of floor measure the apparent weight of body which increases.

 ii. When lift is accelerating downwards:
  When lift is accelerating downwards with an acceleration (a) then,
mg - R = ma
or, R = mg - ma

 Reaction of floor decreases hence apparent weight of person body decreases.

4. Principle of conservation of linear momentum:
   When no external force act on the system of colliding bodies then the total linear momentum of system remains constant (conserved).
 Therefore, F = dp/dt
If F = 0 then, dp/dt = 0
hence, P = constant
or, mv = constant.
  If  two bodies of mass m1 and m2 moving with u1 and u2 collide then their velocities changes to v1 and v2 respectively then,
 m1u1 + m2u2 = m1v1 + m2v2
When two bodies move together after collision then,
 v = (m1u1 + m2u2) / (m1 + m2)


5. Free body diagram:
 While solving the problems relating the newton's law of motion, free body diagram is used. During free body diagram,only the body of our consideration is taken an all the process acting on it are drawn. The net force acting on a body gives the acceleration so, F1 = ma.


6. Rocket propulsion:
 The propulsion of rocket is based on the principle of conservation of linear momentum or newton's third law of motion. A rocket of initial mass M1 eject combust fuel at the rate of dm/dt at any instant at which M be the mass of rocket the velocity of ejected gas relative rocket is v then,
  i. Force on a rocket due to ejection of gas in absence of gravity is, F = dm/dt * v
  ii. Full acceleration on rocket due to this force is, a = F/M = dm/dt * v/M
  iii. Net force on rocket due to gravity, F = dm/dt * v - mg
  iv. Acceleration on rocket in gravity is, a = F/m = dm/dt * v/m - g