Questions from Electronics

Q: On their 21st birthday, one twin gets on a moving sidewalk

On their 21st birthday, one twin gets on a moving sidewalk, which carries her out to star X at speed /her twin brother stays home. When the traveling twin gets to star X, she immediately jumps onto th...

Q: Check Eq. 12.29, using Eq. 12.

Check Eq. 12.29, using Eq. 12.27. [This only proves the invariance of the scalar product for transformations along the x direction. But the scalar product is also invariant under rotations, since the...

Q: (a) Write out the matrix that describes a Galilean transformation

(a) Write out the matrix that describes a Galilean transformation (Eq. 12.12). (b) Write out the matrix describing a Lorentz transformation along the y axis. (c) Find the matrix describing a Lorentz t...

Q: The parallel between rotations and Lorentz transformations is even more striking if

The parallel between rotations and Lorentz transformations is even more striking if we introduce the rapidity: / (a) Express the Lorentz transformation matrix Λ (Eq. 12.24) in terms of θ , and compar...

Q: As an illustration of the principle of relativity in classical mechanics,

As an illustration of the principle of relativity in classical mechanics, consider the following generic collision: In inertial frame , particle A (mass m A, velocity uA) hits particle B (mass m B , v...

Q: (a) Event A happens at point (x A =

(a) Event A happens at point (x A = 5, yA = 3, z A = 0) and at time tA given by ctA = 15; event B occurs at (10, 8, 0) and ctB = 5, both in system S. (i) What is the invariant interval between A and B...

Q: The coordinates of event A are (x A, 0,

The coordinates of event A are (x A, 0, 0), tA, and the coordinates of event B are (xB , 0, 0), tB . Assuming the displacement between them is spacelike, find the velocity of the system in which they a...

Q: (a) Draw a space-time diagram representing a game

(a) Draw a space-time diagram representing a game of catch (or a conversation) between two people at rest, 10 ft apart. How is it possible for them to communicate, given that their separation is space...

Q: (a) Which of the vectors in Problem 1.15

(a) Which of the vectors in Problem 1.15 can be expressed as the gradient of a scalar? Find a scalar function that does the job. (b) Which can be expressed as the curl of a vector? Find such a vector....

Q: Inertial system S¯ moves in the x direction at speed /

Inertial system S¯ moves in the x direction at speed /relative to system S . (The x axis slides long the x axis, and the origins coincide at t= t¯ =0, as usual.) (a) On graph paper set up a Cartesian...