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Physics

System of Particles and Rotational Motion

Motion of Center of Mass

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⚡ Quick Summary
The center of mass of a system moves as if it were a single particle with the total mass of the system, subjected to all the external forces acting on the system.
x = v_x * t, y = v_y * t - 1/2 * g * t^2

The motion of the center of mass of a system is identical to the motion of a single particle of mass equal to the mass of the given system, acted upon by the same external forces that act on the system.

Linear Momentum and Its Conservation Principle

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If the net external force on a system is zero, the total linear momentum of the system remains constant.
p = mv, P = Σ p_i = Σ m_i * v_i

The linear momentum of a particle is defined as p = mv. The momentum of an N-particle system is the vector sum of the momenta of the N particles i.e., P = Σ p_i = Σ m_i * v_i.

If the external forces acting on the system add up to zero, the center of mass moves with constant velocity, which means P = constant. This is known as the principle of conservation of linear momentum.

Rocket Propulsion

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Rockets accelerate by ejecting mass (burnt fuel) at high velocity. The force exerted by the ejected gas propels the rocket forward.
M = M_0 - rt

In a rocket, the fuel burns and produces gases at high temperatures. These gases are ejected out of the rocket from a nozzle at the backside of the rocket. The ejecting gas exerts a forward force on the rocket which helps it in accelerating.