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SYSTEM OF PARTICLE AND ROTATION MOTION

A rigid body is a body with a perfectly definite and unchanging shape. The distances between all pairs of
particles of such a body do not change.

Centre of Mass

  • For a system of particles, the centre of mass is defined as that point where the entire mass of the system is
    imagined to be concentrated, for consideration of its translational motion.
  • If all the external forces acting on the body/system of bodies were to be applied at the centre of mass, the
    state of rest/ motion of the body/system of bodies shall remain unaffected.
  • The centre of mass of a body or a system is its balancing point. The centre of mass of a two- particle
    system always lies on the line joining the two particles and is somewhere in between the particles.

Motion of centre of Mass

The centre of mass of a system of particles moves as if the entire mass of the system were concentrated
at the centre of mass and all the external forces were applied at that point. Velocity of centre of mass of a
system of two particles, ml and m2 with velocity VI and is given
by,

$$V_{cm} = \frac{d r_{cm}}{dt} = \frac{1}{M} \left[m_1 \frac{d r_1}{dt} +m_2 \frac{d r_2}{dt}+ ……+ m_n \frac{d r_n}{dt} \right] $$

$$ = m_1 v_1 + m_2 v_2+ ……..+m_n v_n$$

$$=\frac{\overrightarrow p}{M}$$

or $$\overrightarrow p = M V_cm $$

Mock tests

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