The explanations are written in the attached pdf file.

The two web pages I use as references for formula are
http://en.wikipedia.org/wiki/Lorentz_transformation
and
http://www.wbabin.net/hamdan/hamdan4.htm
However you may not necessarily need them as you likely have all the formula in your textbook(s) or lecture notes.

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Here is the plain TEX source

We shall use the notations
$$
beta = {vover c}
eqno(0.1)
$$
for the dimensionless speed, and
$$
gamma = {1oversqrt{1-beta^2}}
eqno(0.1)
$$
for the Lorentz factor.

bf Q.1rm

Lorentz transformation for the time is
$$
t' = gammal( t - {vxover c^2} r).
eqno(1.1)
$$
As we are requested to have $t'_A = t'_B$ for the two events, from equation (1.1) this requirement

means
$$
gammal( t_A - {vx_Aover c^2} r) = gammal( t_B - {vx_Bover c^2} r).
eqno(1.2)
$$
From equation (1.2) we find the requested difference in times of the events in frame S:
$$
t_A-t_B = {vover c^2} l(x_A-x_Br).
eqno(1.3)
$$

bf Q.2rm

Suppose a particle at $x_1'=0$ is created at $t_1'=0$,
stays at $x_2'=0$ and decays at $t_2' = tau = 1~mu s$ (microsecond).
From the Lorentz transformation back from frame S' to frame S (the same formula as usually ...

Solution Summary

The following posting answers questions about inertial frames.

A.1 Inertial observer O´ moves at speed v in the negative z-direction with respect to inertial observer O.
Write down the relationship between the sets of coordinates used by the two different observers.
A.2 A rocket moves at speed 4c/5 towards the earth. It fires a miss

A sphere consists of a solid wooden ball of uniform density 800kg/m^3 and radius 0.20 m and is covered with a thin coating of lead foil with area density 20kg/m^2 .
Calculate the moment of inertia of this sphere about an axis passing through its center.

Show that the spacetime interval (delta s) is invariant under the lorentz transfermations:
i.e. show that (c (delta t))^2 - (delta x)^s = (c(delta t'))^2 - (delta x')^2
delta s = s1 - s2
delta t = t1 - t2
delta x = x1 - x2
c= speed of light in a vacuum ; 's indicate a different system

(See attached for full problem description)
If electromagnetic wave equation for vacuum is where W is either magnetic B or electric E field vector, show that by using Galilean transformation wave equation will be changed to which has completely different form than given wave equation. Hence, Galilean transformation violate

I need some help answering this question:
A manufacturer of window frames knows from long experience that 5% of the production will have some type of minor defect that will require an adjustment. What is the probability that in a sample of 20 window frames:
A. None will need adjustment?
B. At least one will need adjustment?

See the attached file.
The question starts,
Consider an isolated system comprising two particles of masses m1 and m2. Whose position vectors, in an inertial frame, are x1 and x2 and whose velocity vectors are v1 and v2. The interaction of the particles may be described by an energy function.
E=1/2m1v1^2+1/2m2v2^2+U(x1,x

A manufacturer of window frames know from long experience that 5 percent of the production will have some type of minor defect tht will require an adjustment. What is the probability that in a sample of 20 window frames
a) none will need adjustment
b) at least one will need adjustment
c) More than two will need adjustment

Bolder Bikes, Inc. manufactures mountain bike frames in Boulder Colorado. In 2012, they produced 24,000 frames at a total cost of $1,296,000. Frames Unlimited, Inc. has offered to supply as many frames as Boulder Bikes wants at a cost of $49.50. Boulder Bikes anticipates needing 26,000 frames each year over the next few years.

For what initial velocity and direction of the puck will it (the puck) appear motionless when viewed from above (ie the motionless reference frame).
See attached file for full problem description.
Note for clarification. The initial position refers to the puck is: (x = -.5R, y = 0)

When Time Flies...It Runs More Slowly
Learning Goal: To understand length contraction and time dilation.
In classical physics, and in your everyday experience, lengths and times seem to be the same no matter who measures them. In fact, the notion that lengths or time intervals might be different depending on who measures t