In physics, linear momentum is a vector quantity that is defined as the product of mass and velocity. In simple words, the product of a mass of an object m and its velocity v determines the linear momentum of the object. The alphabet ‘p’ is used to signify momentum in short and combines both m and v. Moreover, the momentum of a body is always in the same direction in which it has a velocity vector. Being a conserved quantity it denotes that the total momentum of a system is constant. The unit of linear momentum is expressed as kg m/s.
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The linear momentum formula is expressed as :
p= m*v
Explain Dimensional Formula of Linear Momentum
We can express the dimensional formula of linear momentum as follows:
[m1 l1 t–1]
Where,
M = mass
L = length
T = time
Derivation
Linear Momentum Formula = mass × velocity. . . . . . (i)
Linear momentum dimensional formula,
Mass = [m1 l0 t0] . . . . (ii)
Velocity = [m0 l1 t-1] . . . . (ii)
By substituting equation (ii) and (iii) in equation (i) we can obtain,
Linear Momentum = mass × velocity
or, L = [m1 l0 t0] × [m0 l1 t-1] = [m1 l1 t-1].
Hence, the dimensional representation of linear momentum is [m1 l1 t-1].
Conservation of Linear Momentum Equation
By applying newton’s second law of motion we can explain the conservation of the linear momentum formula. The rate of change of linear momentum formula of a body is equal to the net force applied to the body.
Mathematically it is expressed as:
dP/dt
= mv/dt
= m dv/dt
= ma
= Fnet
Conclusion
The importance of linear momentum of a body or a system is that it retains the total momentum. This is equal to the product of vector velocity and mass is given that there is no external force acting on it.