Does the centre of mass rotate?

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Syed Aquib Ur Rahman | Contributor-Level 10

6 months ago

Well, the centre of mass is a single point. It does not rotate by itself. But an object or a system of particles can rotate about its centre of mass. The individual particles of a system can move around the centre of mass, and these particles can make the centre of mass move in a straight line at a

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The disc of mass M with uniform surface mass density σ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position (xa/3π, xa/3π) where x is---------. (Round off to the Nearest integer) [a is an area as shown in the figure]

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The x and y coordinates of the center of mass are given by:
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$(0,3)$

$\begin{array}{r} {\overset{?}{r}}_{c m} = \frac{1 \times (\frac{\hat{i}}{2} + \hat{j}) + 1 \times (\hat{i} + \frac{5 \hat{j}}{2})}{2} \\ {\overset{?}{r}}_{c m} = \frac{3}{4} \hat{i} + \frac{7}{4} \hat{j} \end{array}$

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A body of mass 2 kg moving with a speed of 4 m/s, makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is x/10 m/s. Then the value of x is _______ .

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From conservation of momentum:
2×4 = 2v? + mv?
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Payal Gupta

$X_{c} = Y_{c} = \frac{m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3}}{m_{1} + m_{2} + m_{3}} = \frac{m \times 0 + m \times 0 + m \times 3}{3 m} = 1 m$

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How to find shift in centre of mass?

Syed Aquib Ur Rahman

You should know that when the shift in the centre of mass occurs, you can use the principle of moments. With this logic, we can see the shift from the original body as the combination of two parts. The one that remains part and the other that is removed. The formula for the shift is the product of t