Obtain expressions for the center of mass of a system consisting of
(A) two particles
(B) a large number of particles.

Open in App

Solution

Center of mass of two masses

$(m_{1} + m_{2}) x_{c m} = m_{1} x_{1} + m_{2} x_{2}$

For two masses: $x_{c m} = \frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}$

Center of mass for $N$ masses

$M_{t o t} {\to r}_{c m} = \sum_{i = 1}^{N} m_{i} {\to r}_{i} = m_{1} {\to r}_{1} + m_{2} {\to r}_{2} + m_{3} {\to r}_{3} + \dots + m_{N} {\to r}_{N}$

${\to r}_{c m} = \frac{1}{M_{t o t}} \sum_{i = 1}^{N} m_{i} {\to r}_{i} = \frac{m_{1} {\to r}_{1} + m_{2} {\to r}_{2} + m_{3} {\to r}_{3} + \dots + m_{N} {\to r}_{N}}{M_{t o t}}$

$x_{c m} = \frac{\sum_{i = 1}^{N} m_{i} x_{i}}{M} y_{c m} = \frac{\sum_{i = 1}^{N} m_{i} y_{i}}{M} z_{c m} = \frac{\sum_{i = 1}^{N} m_{i} z_{i}}{M}$

Suggest Corrections

Similar questions

m_{1}

m_{2}

m_{1}

m_{2}

m_{1}

m_{1}

m_{2}

L

m_{2}

Join BYJU'S Learning Program