Relativity theory

The relativistic law for velocity addition

$$v = \frac{v_1+v_2}{1+\frac{v_1\cdot v_2}{c^{2}}}$$

v - relativistic velocity (speed)
v1, v2 - speeds in systems
c - speed of light

Find It is known that:

Calculate 'v'

Length (Lorentz) contraction

$$l_{r} = l\cdot \sqrt {1-\frac{v^{2}}{c^{2}}}$$

l_r - relative length
l - length of the object in its rest frame
v - speed (velocity)
c - speed of light

Find It is known that:

Calculate 'l_r'

Time dilation due to relative velocity

$$\Delta_{t_r} = \frac{\Delta_{t}}{\sqrt {1-\frac{v^{2}}{c^{2}}}}$$

Δt_r - time interval in observer system
Δt - time interval in moving system
v - speed (velocity)
c - speed of light

Find It is known that:

Calculate 'Δ_t_r'

Relativistic mass

$$m = \frac{m_0}{\sqrt {1-\frac{v^{2}}{c^{2}}}}$$

m - mass of the moving body
m₀ - rest mass of the body
v - speed (velocity)
c - speed of light

Find It is known that:

Calculate 'm'

Relativistic momentum

$$p = \frac{m_0\cdot v}{\sqrt {1-\frac{v^{2}}{c^{2}}}}$$

p - impulse
m₀ - rest mass of the body
v - speed (velocity)
c - speed of light

Find It is known that:

Calculate 'p'

Einstein's formula

$$E = m\cdot c^{2}$$

E - total energy
m - mass
c - speed of light

Find It is known that:

Calculate 'E'

Einstein's formula

$$E = \frac{m_{0c}^{2}}{\sqrt {1-\frac{v^{2}}{c^{2}}}}$$

E - total energy
m₀ - rest mass of the body
v - speed (velocity)
c - speed of light

Find It is known that:

Calculate 'E'

Total energy of the body

$$E = m_{0c}^{2}+\frac{m_{0v}^{2}}{2}$$

E - total energy
m₀ - rest mass of the body
c - speed of light
v - speed (velocity)

Find It is known that:

Calculate 'E'

Change of energy and mass

$$\Delta_{E} = \Delta_{m}\cdot c^{2}$$

ΔE - change of energy
Δm - change of mass
c - speed of light

Find It is known that:

Calculate 'Δ_E'

Lorentz transformation

$$x_{r} = \frac{x-v\cdot t}{\sqrt {1-\frac{v^{2}}{c^{2}}}}$$

x_r - distance in moving system
x - distance in the rest frame
r - distance
v - speed (velocity)
t - time
c - speed of light

Find It is known that:

Calculate 'x_r'