Here M m m m and Em r is called the first moment of the mass

Last updated: 6/25/2023

Here M m m m and Em r is called the first moment of the mass Further r x i y j z k and TCM XCM YCM 1 ZCM k So the cartesian coordinates of the CM will be or XCM XCM Similarly y CM m x m x mn xn mn m m 11 m x i 1 TCM i 1 M n mi Yi and ZCM m m m3 Substituting the values we get mi zi i 1 M M Example 8 4 The position vectors of three particles of mass m 1 kg m 2 kg and m3 3 kg are r 1 43 k m 1 k m and r3 21 1 2 k m respectively Find the position vector of their centre of mass 5 Sol The position vector of CM of the three particles will be given by m m M3 E3 TCM 91 33 3k 6 n mixi i 1 mi 1 4 k 2 i 3 k 3 21 3 2k 1 2 3 QB x 32 TCM 31 1 k m Example 8 5 Four particles of mass 1 kg 2 kg 3 kg and 4 kg are placed at the four vertices A B C and D of a square of side 1 m Find the position of centre of mass of the particles Sol Assuming D as the origin DC as X axis and DA as Y axis we have Y x y AO