Notes: Relative Motion - WordPress.com

Relative Motion


When observers are moving at a
constant velocity

relative to each
other, we have a case of relative
motion


The moving observers can agree
about
some

things, but not about
everything,

regarding an object they
are both observing

Inertial Reference Frames


Frames of reference which may move relative
to each other but in which observers find the
same value for the acceleration of a third
moving particle.


Inertial reference frames are moving at
constant velocity relative to each other. It is
impossible to identify which one may be at rest.


Newton’s Laws hold only in inertial reference
frames, and do not hold in reference frames
which are accelerating.

Example
: a person on a skateboard throws a ball while a
stationary person watches. The path of the ball will look very
different to these two people.

A particle A is described by two observers:



One observer is in frame S
which is fixed relative to the
Earth


Another observer is in frame
S’ is moving to the right
(relative to S and therefore
the Earth) at v
o


Relative to observer S’, S
moves to the left at
–
v
o


The position of the particle
relative to frame S is r


The position of the particle
relative to frame S’ is r’


r and r’ are related by:


r = r’ +v
o
t or r’ = r
-

v
o
t


Taking equation: r’ = r
-

v
o
t


Differentiating with respect to time: dr’/dt = dr/dt
-

v
o


v’ = v
-

v
o


dv’/dt = dv/dt
-

0


a’=a

This is
Galileo’s Law of
Transformation of Velocities


If observers are moving but not accelerating relative to
each other, they agree on a third object’s acceleration,
but not its velocity!

Sample problem
:

A boat heading due north crosses a river at 10 km/hr relative to
the water. The water in the river moves at 5 km/hr due east
relative to Earth.


a. Find the velocity of the boat relative to an observer


standing on the bank.


b. If this boat has the same speed of 10 km/hr and needs


to head due north in the same river, in which direction


should it steer?


a. 11.2 km/hr at 26.6
°

E of N

b. 30
°

W of N