By Chinmony Taraphdar
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Example 2. The position vectors of points P and Q are given by Fr = 2f + 3J - k, '2 = 4/ - 3J + 2k. k, The Classical Mechanics 30 ~ Determine PQ and its magnitude. or = ~ = 21 + 3J - k. Ans. Here, 00 =- r2 = 41 - 3J+ 2k PO = OO-OP r2 -~ = IpQI = 7 unit. a and b are = 21 -6J+3k. So, its magnitude is Example 3. If (x + 4y)a + (2x + y + I)b and andy 13 = non-collinear vectors and A (y - 2x + 2)a + (2x - 3y - I)b, find x 3A = 213 Ans. Here 3A = 213 such that or, 3(x + 4y)a + 3(2x + y + I)b = 2(y - 2x + 2)a + 2(2x - 3y -I)b a Equating coefficient of and b from both side, 3x + 12y = 2y - 4x + 4 => 7x + lOy = 4 6x + 3y + 3 = 4x - 6y - 2 => 2x + 9x = -S Solving this two equations, x = 2, y = -I.
Conservation of Linear Motion: If no force be applied on a moving particle or system or if the resultant of all applied force be two, then the momentum of that particle or system will be constant. This is principle of conservation* of linear momentum. li = · Smce, . dt "p. '-(Ipi) =0 dt i constant This is conservation of Linear Motion. 11. Time Integral of Force (Impulse) : The time integral of force is basically the impulse of force and it is denoted by j. Mathematically j = If or, * jdJ = r II FCt) dt F, the force be time independent, then J = FM = Force x Time of action This conservation of linear momentum also can be obtained from Newton's 3rd law and so for collision of two particles, mutually colliding or mutually interacting without any applied force, the conservation of linear momentum holds.
T. an arbitrarily choosen origin, '0'. then, mathematically, r when, M = L mi = M Total mass of the body and mj is mass of ith constituent of the body. L mj~ = Mr is the total moment of mass* of that rigid body. Here, Now in actual case, for every constituent particle of a rigid body, two types of force will act on every particle. One is external force and another is internal force, one to mutual interaction with one constituent by other remaining constituent particles. So for ith constituent particle, * For rotation of body about an axis passing through its center of mass, total moment n of mass will be two.
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