Newton's three Law and their Details with math formula. নিউটনের গতিসূত্রসমূহের বর্ণনা এবং গাণিতিক ফর্মুলা।

Newton's first law

According to the first law, if no net force is applied , the stationary object will remain stationary forever and the moving object will continue to move in a straight line or in a straight path with constant velocity. Mathematically, if the net force applied to an object is zero, then the velocity of the object is constant.

\sum \mathbf {F} =0\;\Leftrightarrow \;{\frac {\mathrm {d} \mathbf {v} }{\mathrm {d} t}}=0.

Newton's first law is often referred to as the law of inertia .

Newton's first (and second) formula only applies to inert context structures .

Newton's Second Law

According to the second law, the rate of change of momentum of an object over time is proportional to the applied ball and the change of momentum of the object occurs in the direction in which the force acts.

\mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}}

Constant mass

For objects and systems of constant mass, The second law can be re-stated by the acceleration of the object.

\mathbf {F} ={\frac {\mathrm {d} (m\mathbf {v} )}{\mathrm {d} t}}=m\,{\frac {\,\mathrm {d} \mathbf {v} \,}{\mathrm {d} t}}=m\mathbf {a} ,

Where $F$ is the applied net force, $m$ is the mass of the object, and $a$ is the acceleration of the object. Thus, the net force applied to an object produces proportional acceleration.

Variable-mass systems

Variable-mass systems, such as rocket fuel and gas emissions, are not a closed system and cannot be solved by considering mass in the second formula as a function of time. on an object whose mass $m$ times tend to vary with the emission or attached to the object to get the equation of motion for the mass and the constant mass of the system as a whole, considering the odors or the second formula is applied. As a result,

\mathbf {F} +\mathbf {u} {\frac {\mathrm {d} m}{\mathrm {d} t}}=m{\mathrm {d} \mathbf {v}  \over \mathrm {d} t}

Where $u$ is the velocity of the emitted or incoming mass relative to the object. From this equation are obtained the equations of motion for various variable mass systems, for example, the Tsiolkovsky rocket equations .

In some cases, the left $\mathbf {u} {\frac {\mathrm {d} m}{\mathrm {d} t}}$ Which indicates the rate of change of momentum of the changed mass , its quantity is defined as the force (the force applied to the object by the changed mass, such as the gas emission of the rocket) and is included with the quantity of $F.$ Then the application of the definition of acceleration gives the equation, $F$ = $m$ $a$ .

Newton's third law

According to the third law, balls are always generated in pairs. That is, when an object exerts a force on another object, the second object exerts an equal force on the first object and vice versa. If object A exerts a force F _A on object B , then object B will simultaneously apply force - F _B on object A , and the values of the two balls are equal and opposite: F _A = - F _B