Centre of Mass

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The centre of mass is the point whose motion characterises the motion of the whole system. When a system moves under an external force, it moves as if the entire mass were concentrated at this point a…

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\left(m_{1}+m_{2}\right) \overrightarrow{\mathbf{r}}_{c m}=m_{1} \overrightarrow{\mathbf{r}}_{1}+m_{2} \overrightarrow{\mathbf{r}}_{2} Here, m1 and m2 are the masses, r1 and r2 are their position ve…

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\overrightarrow{\mathbf{r}}_{c m}=\frac{m_{1} \overrightarrow{\mathbf{r}}_{1}+m_{2} \overrightarrow{\mathbf{r}}_{2}}{m_{1}+m_{2}} This is a weighted average of the position vectors.

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Given: - m1 = 0.5 kg, r1 = (-1, 2) - m2 = 1 kg, r2 = (3, 4) Use component form: - x_cm = [m1 x1 + m2 x2] / [m1 + m2] - y_cm = [m1 y1 + m2 y2] / [m1 + m2] Step 1: x_cm = [(0.5 kg)(-1) + (1 kg)(3)] / …

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The position vector of the centre of mass is a weighted mean of the two position vectors. Since both masses are positive, the weighted average lies on the line joining the two particles and between th…

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\overrightarrow{\mathbf{r}}_{c m}=\frac{\overrightarrow{\mathbf{r}}_{1}+\overrightarrow{\mathbf{r}}_{2}}{2} Thus, the position vector of the centre of mass of two particles of equal masses is the av…

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If r_cm = 0, then m1 r1 + m2 r2 = 0. That is, the sum of the moments of the masses of the system about the centre of mass is zero.

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\overrightarrow{\mathbf{r}}_{c m} =\frac{1}{M} \sum_{i=1}^{n} m_{i} \overrightarrow{\mathbf{r}}_{i} Here, mi is the mass of the ith particle, ri is its position vector, and M is the total mass.