law of conservation of momentumlaw
The law was formulated by Newton in the Principia (1687) based on the work of Wallis, Wren, and Huygens on collisions. It states: if no external forces act on a system, total momentum is conserved. The reason is the homogeneity of space: the laws of physics do not depend on where you are, and from this symmetry (by Noether's theorem) follows conservation of momentum. Analogy: on perfectly smooth ice, a skater who throws a backpack will move in the opposite direction — without external friction, the motion of the system's center of mass does not change.
How it works
A figure skater pushes off the barrier: she gains momentum in one direction, while the rink together with the Earth — negligibly small due to the huge mass — in the other. In a firework, the gunpowder gases fly downward, and the rocket upward. When shooting, the recoil of the weapon is a consequence of the law: the bullet and the rifle receive equal but opposite momentum.
💡 In open space, if an astronaut throws a wrench away from themselves, they will start drifting slowly in the opposite direction, while the wrench flies forward. Retrieving the wrench without assistance is impossible — momentum is already divided.
p = m v
p — momentum of the body (kg·m/s); m — mass of the body (kg); v — velocity of the body (m/s)
m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2
m₁, m₂ — masses of the first and second bodies; u₁, u₂ — their velocities before interaction; v₁, v₂ — their velocities after interaction.