Physics · System Of Particles And Rotational Motion · NEET
No. Momentum is a vector, so you must add the momentum vectors, not the numbers. Two equal particles moving in opposite directions each have momentum p, but the system total is p - p = 0, not 2p. Always break into components (x and y) and add signed values. In the 2026 NEET PYQ two particles on a ring gave P = 2mv*|cos theta| exactly because the perpendicular parts cancelled and only the parts along the diameter added.
By definition, the centre of mass position is R(cm) = (m1*r1 + m2*r2 + ...)/M. Differentiate with respect to time: M*V(cm) = m1*v1 + m2*v2 + ... which is exactly the total momentum P. So P = M*V(cm) is not a new rule, it just follows from the definition of centre of mass. This lets you replace a messy many-particle system with a single point of mass M.
No. Internal forces always come in Newton's third-law pairs (equal and opposite), so they cancel when you add them over the whole system. Only the net external force can change P. The equation is dP/dt = F(external). This is why an exploding shell's centre of mass keeps moving on the same path even though the pieces fly apart.
A single particle has p = m*v, one mass and one velocity. A system has many particles, and its momentum is the vector sum of all of them, which equals M*V(cm). The individual particles can speed up, slow down, or collide, but as long as no external force acts, the system momentum P stays fixed.
When the net external force is zero, dP/dt = 0, so P is constant. This is conservation of linear momentum. Collisions, explosions, and recoil (gun-bullet) are the classic NEET cases where external force is negligible during the short interaction, so P before equals P after.
A frictionless circular wire of unit radius lies in a horizontal plane. Two point particles of unit mass start simultaneously from A (theta = pi/2) with identical uniform angular speeds in opposite directions and meet again at B (theta = -pi/2). Which figure best represents the magnitude of the total linear momentum P of the system as a function of theta?
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The same as for one particle: kilogram metre per second (kg m/s), because it is just a sum of m*v terms. In terms of force it is also newton-second (N s).
It is always true. P = M*V(cm) comes directly from the definition of the centre of mass, so it holds whether or not external forces act. Conservation (P constant) is the special case when the net external force is zero.
Yes. If the momenta cancel as vectors, the total is zero even though each particle moves. Example: two equal masses moving with equal and opposite velocities, or the two ring particles at the start and meeting points in the 2026 PYQ.
Mainly through conservation of momentum in collisions, explosions and recoil, and through P = M*V(cm) to find the centre-of-mass velocity of a group of particles. Both appear almost every year in System of Particles.
