# Einstein's energy equation and kinetic energy

Why is the kinetic energy given by $$E=\frac{1}{2}mv^2$$
yet Einstein's energy equation is $$E=mc^2$$?
Why is there a different constant (ie $$\frac{1}{2}$$ and $$1$$)?

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ZapperZ
Staff Emeritus
dirtydog said:
Why is the kinetic energy given by $$E=\frac{1}{2}mv^2$$
yet Einstein's energy equation is $$E=mc^2$$?
Why is there a different constant (ie $$\frac{1}{2}$$ and $$1$$)?
Er... because they are NOT the same beast, so why should they be identical? One is the energy of motion, the other is the REST mass energy.

Zz.

arildno
Homework Helper
Gold Member
Dearly Missed
You are confusing relativistic energy with classical kinetic energy.
If I remember correctly, the relativistic energy of a particle with rest mass m is given by:
$$E_{rel}=\frac{mc^{2}}{\sqrt{1-(\frac{v}{c})^{2}}}\approx{m}c^{2}+\frac{1}{2}mv^{2},v<<c$$
(where v is the measured velocity of the particle)

In the low speed limit, we see that the relativistic energy can be written as the sum of the rest mass energy ($$mc^{2}$$) and the classical kinetic energy.

Last edited:
hi dirtydog,
as zapperz says, thery are not the same thing. kinetic energy (KE) is a form of energy that a body has due to its motion, while the other eqn describes the total amt of inherent energy that a body has due to its mass.

therefore for the KE, a body's KE can be increased by increasing its speed. a drop in speed would therefore cause the KE to drop. an obj at rest would then hav 0 KE.

as for E = mc^2, no matter the body is moving or not, the E here remains the same if the body's mass does not change. u can onli vary this E by varying the mass of that body. therefore this eqn gives u the total amt of energy that is 'associated' with a certain mass.

hope that helps to clarify things.