University Physics I - Classical Mechanics, 2019

184 CHAPTER 8. MOTION IN TWO DIMENSIONS
8.7.3 Rotating frames of reference: Centrifugal force and Coriolis force
Imagine you are inside a rotating cylindrical room of radius R. There is a metal puck on the floor,
adistancer from the axis of rotation, held in place with an electromagnet. At some time you
switch off the electromagnet and the puck is free to slide without friction. Find where the puck
strikes the wall, and show that, if it was not too far away from the wall to begin with, it appears
as if it had moved straight for the wall as soon as it was released.
Solution
The picture looks as shown below, to an observer in an inertial frame, looking down. The puck
starts at point A, with instantaneous velocity ωr pointing straight to the left at the moment it is
released, so it just moves straight (in the inertial frame) until it hits the wall at point B. From the
cyan-colored triangle shown, we can see that it travels a distance √ R 2 − r 2 , which takes a time
√
R
Δt =
2 − r 2
ωr
In this time, the room rotates counterclockwise through an angle Δθ room = ωΔt:
(8.62)
Δθ room =
√
R 2 − r 2
r
(8.63)
A‘
B
A
B‘ R
r
O
Figure 8.10: The motion of the puck (cyan) and the wall (magenta) as seen by an inertial observer.
This is the angle shown in magenta in the figure. As a result of this rotation, the point A’ that was
initially on the wall straight across from the puck has moved (following the magenta dashed line)
to the position B’, so to an observer in the rotating room, looking at things from the point O, the
puck appears to head for the wall and drift a little to the right while doing so.