Newton’s Laws of Motion: First Law of Motion

Among Newton’s Laws of Motion, first law of motion states that,

“Body tries to maintain its state of rest or uniform motion along the straight line, until and unless an unbalanced force acts on it.”

This is the property of object to keep it self in state of rest called inertia. Hence, this newton’s law is also known as law of inertia. Inertia is directly proportional to mass. Larger the size of object higher will be the inertia. Some common examples of newton’s first law of motion are

1. In a bus, body remains in state of rest. As soon as, driver applies brakes, motion of bus slows down and body maintain its state of rest.
2. While taking a sharp turn body gets thrown towards opposite, because body tries to maintain its motion in straight line.
3. When bus starts, body fall slightly backward thereby experiencing jerk. This happens because feet are in contact with bus, when bus start they experience motion. But rest of body is at rest due to which body tries to fall backward.

Newton’s Laws of Motion: Second Law of Motion

Among Newton’s Laws of Motion, second law is based on momentum. Momentum is product of mass and velocity.
P = mv
Momentum is vector quantity having magnitude and direction. Moreover, direction of momentum is same as direction of velocity. Therefore, Newton’s second law of motion states that,

“Rate of change of momentum of object is directly proportional to force applied on body in direction of force.”

Newton’s Law of Motion: Second Law of Motion

Mathematical derivation of second law of motion

Consider an object of mass m, moving in a straight line with initial velocity u. It shows uniform acceleration to velocity v in time t. Let F be force applied on the body. Let p1 = mu and p2= mv be initial and final momentum respectively.



Therefore,
Change in momentum ∝ p2 -p1
                                    ∝ mv – mu
                                    ∝ m × (v – u)
Rate of change of momentum ∝ [m × (v – u)] / t
Therefore,
Force F ∝ [m × (v – u)] / t
             = [k m × (v – u) ] / t ….. [ k is constant of proportionality ]
          F = k m a ….. [∵ a = (v – u) / t ]
The value of k is one. Hence, one unit force is defined as an amount that produces acceleration of 1 m s-2 in an object of mass 1 kg
∴ one unit force = k × 1 kg × 1 ms^-2
∴ F = ma
The unit of force is kg ms^-2 or newton denoted by symbol N.
Force acting on an object can be defined as

“The product of mass of an object to product of acceleration of an object.”

Newton’s Laws of Motion: Third Law of Motion

Third Newton’s Laws of Motion states that,

“Every action has equal and opposite reaction.”

Various daily examples satisfy newton’s third law of motion. A gun when fired releases bullet out of it. If observed carefully bullet from the gun moves forward whereas, gun recoils backward. Moving of bullet in forward direction is action whereas, recoil of gun in backward direction is reaction. Some similar examples are:

1. Flying of birds: Flying of bird is possible due to motion of wings. Wings moves in downward direction and push the air. Air in return exerts pressures thereby, moving the bird upward. Here, motion of wings to push air is action whereas, pushing of bird upward due to air pressure is reaction.
2. Motion of rocket: Rocket exhaust exerts pressure on ground. Ground exerts equal and opposite pressure thereby lifting the rocket in upward direction.

Keywords: Newton’s first law of motion, Newton’s second law of motion, Newton’s third law of motion, Force, momentum, inertia, law of inertia

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