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| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
|---|---|---|---|---|---|---|
| 18.6 | Relativistic Dynamics. Mass, Impulse and Energy in Relativity |
In these revision notes for Relativistic Dynamics. Mass, Impulse and Energy in Relativity, we cover the following key points:
When a particle moves very fast (v → c), it resists more and more to any change in velocity. This means its mass increases with the increase of velocity. In other words, in relativistic events mass does not remain constant but increases with the increase in velocity according the function m = m(v⃗) such that m → ∞ when v → c.
Since the length of objects in relativistic events experiences contraction, there must be an increase in mass at the same rate The rate of mass increase is the equal to that of length decrease. Therefore, we obtain the following equation for the relativistic mass
where m is the relativistic mass of particle, m0 is the classical mass (rest mass), and v is the velocity of particle in the system S. This means we obtain for the relativistic impulse
This formula still contains the relationship between impulse, mass and velocity but now this relationship is not anymore linear. The above two formulae are closely related to each other and are known as the relativistic formulae of mass and impulse. They are valid for all objects - whether microscopic or macroscopic.
If v = 0, then m0 = m. This means the Newtonian mass m0 (otherwise known as the rest mass m0) is nothing else but the relativistic mass of particle in an inertial system where the particle is at rest. For v → c the mass and impulse point towards infinity (m → ∞, p → ∞). Hence, the velocity v = c is as a barrier for material particles.
Energy in relativistic events is represented by two terms: one classical and the other relativistic. The equation of energy in relativistic events is
When the particle is observed in the system S', we obtain
From the above equation, we conclude that energy and impulse are relativistic quantities; their values depend on the system of reference used to study the motion. However, the difference of squares of energy and the corresponding p · c terms is constant. This helps us find the energy and impulse formulae when switching from one inertial system to another.
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