Inertial Coordinate Systems

pleasehelpmath

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A train moves due West at a constant speed v. It passes a carousel two
mile due South of the carousel at 1:00 p.m. Consider two coordinate systems
with origin the central point about which the carousel rotates. The rst
system, X = (x1; x2), is stationary and is oriented in the usual East-West,
North-South fashion, but the second system is attached to the carousel, which
is rotating counterclockwise with constant angular speed ! with respect to
X. The rotating system is denoted by Yt = (yt1; yt2), and at 1:00 p.m. t = 0
and Yt = Y0 = X.
(a) Find a matrix O such that X(p)T = OYt(p)T for each point p in space.

O = (cos(tw) -sin(tw)
sin(tw) cos(tw))



(b) Find the position of the train as a function of t as measured by both X
and Yt:

So I know that the train moves along the direction vector (cos(pi), sin(pi))
so... positionx(t) = (0, -2) + tv(1,0) = (tv, -2)
then does positiony(t) = (cos(tw) -sin(tw) (tv
sin(tw) cos(tw)) -2)

(c) Find the velocity of the train in both systems.

I could do this part if I had both positions (stationary and moving one), but not confident in part (b)
(d) Let Z be a coordinate system attached to the train oriented in the usual
north-south, east-west fashion. Find the relation linking Z coordinates to
those of X:



(d) Which of the three coordinate systems are inertial? Why?

I know how to determine if X, Y, Z are inertial, but not sure what X, Y, and Z are.


(e) A bird is spotted at X = (0; 0)
ying with speed u on a course 45o east of
due north as viewed by the stationary observer X: Find its position vector
relative to X;Y; and Z:
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,786
That's a lot to read. I found myself hoping you would demonstrate YOUR work or YOUR thoughts or impressions. That IS where we need to start.
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,134
A train moves due West at a constant speed v. It passes a carousel two
mile due South of the carousel at 1:00 p.m. Consider two coordinate systems
with origin the central point about which the carousel rotates. The rst
system, X = (x1; x2), is stationary and is oriented in the usual East-West,
North-South fashion, but the second system is attached to the carousel, which
is rotating counterclockwise with constant angular speed ! with respect to
X. The rotating system is denoted by Yt = (yt1; yt2), and at 1:00 p.m. t = 0
and Yt = Y0 = X.
(a) Find a matrix O such that X(p)T = OYt(p)T for each point p in space.

O = (cos(tw) -sin(tw)
sin(tw) cos(tw))



(b) Find the position of the train as a function of t as measured by both X
and Yt:

So I know that the train moves along the direction vector (cos(pi), sin(pi))
so... positionx(t) = (0, -2) + tv(1,0) = (tv, -2)
then does positiony(t) = (cos(tw) -sin(tw) (tv
sin(tw) cos(tw)) -2)

(c) Find the velocity of the train in both systems.

I could do this part if I had both positions (stationary and moving one), but not confident in part (b)
(d) Let Z be a coordinate system attached to the train oriented in the usual
north-south, east-west fashion. Find the relation linking Z coordinates to
those of X:



(d) Which of the three coordinate systems are inertial? Why?

I know how to determine if X, Y, Z are inertial, but not sure what X, Y, and Z are.


(e) A bird is spotted at X = (0; 0)
ying with speed u on a course 45o east of
due north as viewed by the stationary observer X: Find its position vector
relative to X;Y; and Z:
An inertial co-ordinate system has NON-ACCELERATING origin.
 
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