Specialioji reliatyvumo teorija: Skirtumas tarp puslapio versijų

:<math>mv^2+\int_0^v\frac{m_0 c^2}{2\sqrt{1-\frac{v^2}{c^2}}}d(1-\frac{v^2}{c^2})=mv^2+\Big(m_{0}c^2\sqrt{1-\frac{v^2}{c^2}}\Big)\Big|_0^v=mv^2+m_{0}c^2\sqrt{1-\frac{v^2}{c^2}}-m_{0}c^2;</math>
:<math>E_k\approx mv^2+m_0 c^2(1-{1\over 2}\frac{v^2}{c^2})-m_{0}c^2=mv^2+m_0 c^2-{m_0 v^2\over 2}-m_{0}c^2=mv^2-{m_0 v^2\over 2}={mv^2\over 2}={m_0 v^2\over 2},</math> kai greitis <math>v</math> nerealitivinis (daug mažesnis nei šviesos greitis).
<math>E_k=mv^2+m_{0}c^2\sqrt{1-\frac{v^2}{c^2}}-m_{0}c^2=mv^2+m_{0}c^2\sqrt{1-\frac{v^2}{c^2}}{\sqrt{1-\frac{v^2}{c^2}}\over \sqrt{1-\frac{v^2}{c^2}}}-m_{0}c^2=mv^2+mc^2 \sqrt{1-\frac{v^2}{c^2}}\sqrt{1-\frac{v^2}{c^2}}-m_{0}c^2=mv^2+mc^2 (1-\frac{v^2}{c^2})-m_{0}c^2=mc^2-m_0 c^2=m_0 c^2\over\sqrt{1-\frac{v^2}{c^2}}}-m_0 c^2,</math> kai <math>v=0</math> (arba mažas, reliatyvistinis, neįtakojantis).
<math>=mv^2+mc^2 (1-\frac{v^2}{c^2})-m_{0}c^2=mc^2-m_0 c^2=m_0 c^2\over\sqrt{1-\frac{v^2}{c^2}}}-m_0 c^2,</math> kai <math>v=0</math> (arba mažas - nereliatyvistinis).
 
Dydį ''m''<sub>0</sub>''c''<sup>2</sup> pavadinsime [[rimties energija]]. Tada gauname, kad:
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