Question 3: What is linear momentum? Derive and state Newton’s second law in terms of linear momentum.

Answer

Linear Momentum

When an object is moving with a certain velocity, it is exerting force on some other body which tries to stop it. Larger the mass or speed, more difficult it is to stop it. Newton called this feature of material objects as quantity of motion. This is now called linear momentum. Physically, linear momentum is equal to the product of the mass of the body and its velocity.

If m is the mass of the body moving with velocity , then the mathematical expression for its linear momentum is given by,

Linear momentum is a vector quantity and its direction is along the direction of the velocity of the body. Its unit as clear from the above equation is kg m/s. (Show that kg ms^{-1} = N s).

Similarly, dimension of linear momentum is = [MLT^{-1}].

Newton's Second Law in terms of linear momentum

Newton’s Second Law of Motion is

Acceleration is rate of change of velocity.

So putting this value of acceleration in equation (1),

Since,

therefore,

Force applied = Rate of change of momentum.

This is Second Law of Newton in terms of linear momentum.

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