Mechanics | Relativity Answers

1.    A particle of mass m moves in the x y-plane. Its position vector as a function of time is given by  where ω = angular velocity of the Find Velocity

1.      The equation in polar coordinates of an ellipse with semi-axes a and b is:

You will find the size and field of action of the resultant of two parallel forces with sizes 40N and 60N, whose impactors are at a distance of 2m. The forces act: a, In the same direction b. In the opposite direction

 The wheel with the load weighs 120kg. The center of gravity of the wheel is at a distance of 40 cm from the axis of rotation. With what force do we lift the wheel if the end of the hands is at a distance of 1.2 m?

Derive Maxwell equations in four vector notation using anti-symmetric electromagnetic 

field tensor F^𝝁𝝂 = 𝝏^𝝁𝑨^𝝂 − 𝝏^𝝂𝑨^𝝁.

A certain line in the spectrum of the light from a nebula has a wavelength of

656 nm instead of the 434 nm measured in the laboratory. If the nebula is moving

radially, what is its speed relative to the Earth? Ans.: It is moving away from the

Earth with a speed of V ¼ 0:391c.

 The Sun has a radius of 7:0  108 m, approximately, and a period of rotation

about its axis equal to 24.7 days. What is the Doppler shift of a spectral line with

laboratory wavelength 500 nm, in the light emitted (a) from the center of the Sun

and (b) from the edges of the Sun’s disk at its equator?

Ans.: (a) Dk ¼ 1:8  10
8 nm, (b) Dk ¼ 

0:00344 nm

light source moves in a circular orbit with a speed of 0.5c. What is the

displacement, due to the Doppler effect, of the sodium yellow line, as observed at

the center of the circle? The line has a wavelength of 589 nm in the laboratory.

Ans.: Dk ¼ 91 nm

A spaceship moves with speed V relative to an observer O, on a straight line

which passes very near the observer. A source on the spaceship emits light of

wavelength kO ¼ 500 nm in the frame of reference of the spaceship. For what range

of the spaceship’s speed will the light be visible to the observer? The wavelengths of

visible light stretches from kA ¼ 400 nm to kB ¼ 700 nm, approximately.

Show that the light from a source which is moving away from us with a speed of

0.6c has twice the wavelength it has in the frame of reference of the source.