Video Transcript
Thin layers of equal area and
thickness of two different-colored oils are placed onto the central region of the
top surface of two identical solid disks, as shown in the diagram. The disks are then rotated with
equal angular velocities and the oils spread over the surface of the disks. The oils have the same density but
different viscosities. Which of the oils has the greater
viscosity?
Okay, so we see in our diagram
these two disks. And we’re looking at them in what
we could call before and after instances. First, we have the two discs
stationery and these two oils are deposited onto the center regions of each one. We could call the oil on the top
desk the orange oil and that on the bottom disk the yellow one. We’re told that the regions on
these disks that are covered by the oils are of equal area and equal thickness. This means that the oil volumes are
the same. So, there’s just as much orange oil
on this disk as there is yellow oil on this one. And they cover the same amount of
area at the center of each identical disk.
So, this is our before
scenario. And then, the disks are set to
rotating. Our problem statement tells us that
they rotate with equal angular velocities, in other words, the same angular
speed. And as a result of this, the two
oils spread out over the surface of the disks. The oils, we’re told, have the same
density, but they have different viscosities, that is, thicknesses. Based on how these two different
oils respond to the rotation of these disks, we want to identify which one has the
greater viscosity.
To begin figuring this out, we can
recall that viscosity indicates the internal friction of a fluid. That is, the more friction between
the layers of that fluid, the higher its viscosity is. We can also say that if the layers
of a given fluid have a lot of friction between them, then it will be unlikely for
those layers to move very much relative to one another. That’s because there’s such a
strong resistance to movement through friction. So, related to our question, the
oil with the greater viscosity will be the one that moves less or, we could say,
deforms less in response to the rotation of these disks.
That will be the oil that, we could
say, is held together more closely than the less viscous of the two oils. So, looking at this snapshot of our
spinning disks, after the oils have had a chance to expand across those surfaces, we
see that it’s the orange oil that has expanded less than the yellow one. That means this oil more strongly
resists deformation and that resistance, we can assume, is due to higher levels of
internal friction in this oil. In other words, this is the more
viscous of the two. For our answer then, we can say
that the orange oil has greater viscosity. And we say that because this oil
was deformed the least of the two.
