Definition of force from Newton's first law of motion
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You have understood from Newton's first law that change in motion is caused due to an external force. We are now in a position to define force.
Force
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Is the push/pull which changes or tends to change the state of rest or uniform motion in a straight line. It is a vector quantity, i.e., it has both magnitude and direction.
Inertia
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As we have defined earlier, inertia is the property of objects to remain at rest or uniform motion unless acted upon by a force. Three types of inertia are observed.
Inertia of rest
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Property due to which a body tends to remain at rest.
Example of Inertia of rest:
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A coin placed on top of a card remains in place when the card is slightly and quickly jerked horizontally.
Inertia of motion
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Property due to which a body maintains its state of uniform motion.
Example of Inertia of motion
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If a person jumps outside a moving bus and tries to stop immediately, he falls. This is because his body still tends to move forward with the velocity of the bus but his feet are stationary.
Inertia of direction
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Property due to which a body maintains its sense of direction.
Example of Inertia of direction
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A ball rolled on a horizontal floor continues to move in a straight line.
Momentum
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Consider a car and a bicycle moving at the same velocity. Now, if you could somehow use the same brake system on both vehicles, the bicycle will stop first. Why do think so?
Is it because the bicycle is lighter?
Yes, it is because the bicycle is lighter.
This makes us think of a new property of a body in motion. This property is momentum. Momentum is the quantity of motion possessed by a moving body.
Momentum of a body is defined as the product of its mass and its velocity.
Momentum <span style="font-family: Serif;">ρ→</span> = m <span style="font-family: Serif;">v→</span>
The mass of the body is 'm', which is a scalar and the velocity <span style="font-family: Serif;">v→</span> is a vector. Hence, the direction of momentum <span style="font-family: Serif;">ρ→</span> is the same as the direction of velocity <span style="font-family: Serif;">v→</span> . The SI unit of momentum is (kg x m/s) or kg m/s.
From the above expression, we can understand that when two bodies have equal velocities then the heavier body has greater momentum. Similarly, when two bodies have equal mass, the faster body has greater momentum.
Now consider a situation where two bodies of different masses are acted upon by a constant force for an equal amount of time. They both gain different velocities at the end of it. Newton noticed that the magnitude of momenta of both the bodies were equal. This observation led to Newton's second law of motion.
