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Recently I studied the concept of cyclotron. In the limitations part of the topic, it was mentioned:

The mass of the particle increases with increase in number of revolutions.

The book had given the formula: $$m=\frac { { m }_{ 0 } }{ \sqrt { 1-\frac { { v }^{ 2 } }{ { c }^{ 2 } } } } $$

I couldn't understand how the mass of the particle increases. Can anyone explain me why this happens? Is there a method to derive the above equation?

Talking about what I've tried, I couldn't think of a concept with which I could proceed.

Thanks.

Aditya Kumar
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    It's not the mass that increases, but it's resistance to acceleration. You might want to read up on special relativity. – pfnuesel Feb 15 '16 at 16:28
  • @pfnuesel can you explain please? I don't know much about special relativity. But what is the formula there for? – Aditya Kumar Feb 15 '16 at 16:30
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    About the mass thing: http://physics.stackexchange.com/questions/133376/why-is-there-a-controversy-on-whether-mass-increases-with-speed . While correct physics can be done using the concept it will causes you more confusion than it is worth. – dmckee --- ex-moderator kitten Feb 15 '16 at 21:33

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The formula that you have been given has to do with relativity. As a particle continues to move faster and faster, its mass/energy increases by a factor called \gamma .

With each half revolution in the cyclotron, the velocity increases and so in turn does the mass/energy of the particle.

Jaywalker
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  • See the link I offered in the comments to the question. Most working physicist don't use the relativistic mass concept anymore for a number of reasons among which is that it is a pedagogical nightmare that encourages all kinds of misconceptions. – dmckee --- ex-moderator kitten Feb 15 '16 at 21:34