20180302 - Relative Motion and Velocities

Tuesday, 27 February 2018

4:38 PM

Machine generated alternative text:
Relative motion and velocities
(Galilean/ Newtonian r&lativity: watch for hidden assumptions)
Origin of frame (x',y') is at üand moves with ÜfWith respect to (x,y) frame.
¯ at
dt
Think: Vover the ground
dt r f
river over ground + V
you over river

True Velocity

Uniform circular motion

Speed is unchanging

Angular speed is unchanging

Where is the angular speed - constant for uniform circular motion

Extraction Proof

Machine generated alternative text:
y (t+At)
r (t+At)
rA()
AO
0
(Make the triangle very thin)
As At and AO- 0, —> right angles to 13
so
is parallel to -F
lim —
Y (t+At)
x
Acceleration towards the centre:
centripetal acceleration
= -1 *radial acceleration
Now let's get the magnitude of 13 and d:
zls= rA0
so v =
dt
[definition of angle)
— r — = rw as before
dt