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11TH GRADE · SPECIAL RELATIVITY

Relativistic effects

Changes in mass, time and length at high speeds.

24 minutes11 theory cards
Open interactive lesson

LESSON MATERIAL

Basic Concepts

2

Special relativity

Theory of space and time for inertial reference systems, taking into account the invariance of the speed of light.

It is based on two postulates: the laws of physics are the same in all inertial systems, and the speed of light in a vacuum is the same for all observers.

Relativistic effects

Changes in measured time, length, energy and momentum at speeds comparable to the speed of light.

They become noticeable only at speeds close to c; The body's own weight remains unchanged, but energy and momentum increase.

LESSON MATERIAL

Physical quantities

6

Relativistic mass (historical record)

mm

Speed-dependent quantity γm₀; in the modern formulation, the rest mass is considered invariant, and the change is described in terms of energy and momentum.

Unit: kilogram · kg\mathrm{kg}

Rest mass

m0m_0

The mass of a body in the frame of reference where it is at rest.

Unit: kilogram · kg\mathrm{kg}

Observer time interval

τ\tau

The interval between events in the reference frame relative to which the clock moves.

Unit: second · s\mathrm{s}

Own time

τ0\tau_0

The duration of a process in a system where events occur at one point.

Unit: second · s\mathrm{s}

Longitudinal length of a moving body

ll

The length of the body along the movement in the chosen reference system.

Unit: meter · m\mathrm{m}

Own length

l0l_0

The length of a body in the frame of reference where the body is at rest.

Unit: meter · m\mathrm{m}

LESSON MATERIAL

Lesson formulas

3

Relativistic mass (historical record)

m=m01−v2c2m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}

In the outdated convention, the value m = γm₀ increases as the speed approaches c; the modern approach leaves the mass m₀ unchanged.

Condition: Use only if the condition explicitly assumes relativistic mass. Modern recording usually works with energy and momentum.

Time dilation

τ=τ01−v2c2\tau=\frac{\tau_0}{\sqrt{1-\frac{v^2}{c^2}}}

The observer measures a larger interval τ between events on a moving clock than his own interval τ₀.

Condition: τ₀ is measured by the clock located at the same point as both events; v is the speed of this clock relative to the observer.

Length reduction

l=l01−v2c2l=l_0\sqrt{1-\frac{v^2}{c^2}}

The longitudinal length of a moving body is less than its own length.

PRACTICE

Tasks on the topic

Special relativity11 class · 5 problems