Velocity of centre of mass in centre of mass frame is considered zero. But how are the two contradictory statements written in the book?
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2$\begingroup$ isn't zero also a constant? The first statement is the special case of the second one $\endgroup$– Aslan MonahovCommented Sep 24, 2022 at 1:17
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5$\begingroup$ Please do not post images of texts you want to quote, but type it out instead so it is readable for all users and so that it can be indexed by search engines. For formulae, use MathJax instead. $\endgroup$– Níckolas AlvesCommented Sep 24, 2022 at 1:24
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$\begingroup$ You can show (but it requires a little work) that the velocity of the center-of-mass is always constant, as long as there are no external forces. Because the velocity is constant you can always boost to an inertial frame (called the center-of-mass System frame of reference in your screenshot) where the center-of-mass velocity is zero. $\endgroup$– hftCommented Sep 24, 2022 at 1:30
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3 Answers
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In the absence of any external forces, the velocity of the center of mass is constant in any inertial reference frame. The particular constant will depend on the reference frame.
On the center of mass frame, the constant is zero.
answered Sep 24, 2022 at 1:24
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In CM frame, the centre of mass is considered at rest at the origin. But with respect to the lab frame, it is moving with a constant velocity.
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From ground frame, the centre of mass does have a velocity. From the reference frame of the centre of mass itself, its (relative) velocity is zero.
Imagine you are standing on the ground, and a car passes by. Do you see the car moving with a velocity? Yes. To the driver of the car, however, it would appear that the car is at rest, and you and your surroundings are going backwards, which means the velocity of the car relative to itself is zero.
