Background boosters for elementary teachers
Q: Why don’t all rolling objects
reach the bottom of an incline at
the same time?
By Bill Robertson
A Rolling Race
Now, when you let objects roll down
an incline, what causes them to go
to the bottom? If you said gravity,
you win the lovely prize behind the
curtain where Carol is now standing. (This is a reference for all of us
old enough to have watched Let’s
Make a Deal when we were kids.)
If gravity is responsible for objects
falling straight down, where objects
reach the ground at the same time
and gravity is responsible for objects
62 Science and Children
brian diskin
A:
If there’s one thing most people have learned about motion, it’s that as long as there’s not
significant air friction, all dropped
objects reach the ground at the same
time. That’s because gravity, which
is responsible for the objects falling,
is an equal opportunity accelerator.
Objects with different masses hit the
ground at the same time. To prove
this to yourself, drop a paper clip
and a box of paper clips onto a carpeted surface (hard surfaces break
the box, and who wants to do that?).
If you release them at the same time
and from the same height, they will
hit the ground at the same time. I’m
not going to go into the reason for
that right now because that’s a column all by itself. Let’s just accept
that as an observation.
“Not bad....Twenty bucks says my logs will roll down faster than your sewer pipes!”
rolling down an incline, shouldn’t all
objects rolling down an incline reach
the bottom at the same time? Well,
let’s test that. Get yourself a large
clean surface, such as a large sheet
of cardboard or a wooden board or
whatever you can find around the
house. Support it on one end to create an incline. Don’t make it too steep
(Figure 1). Now gather a number of
rolling objects. I used a Ping-Pong
ball, a golf ball, a marble, a tennis
ball, and a socket that’s used in socket
wrenches. I chose these because they
clearly have different masses, and for
another reason I’ll explain later. Now
find a ruler or similar object that can
hold all your rolling objects at the
top of the incline and that you can
remove easily to let the objects have
a fair start in their race down the incline. Again, see Figure 1.
Before you start the race, make a
quick prediction as to which object
will win the race and which object
will come in last. Of course you might
predict that all the objects will tie, but
you’ll be wrong about that. Set the objects at the top of your incline and remove your ruler or other device. Try to
determine not just which objects win
and lose the race, but also the order of
finish. To determine this, you might
have to race the objects a number of
times, and you might have to decrease
the steepness of your incline.
Here are the results I got. The golf
ball won the race, with the marble
coming in second, the tennis ball
third, the Ping-Pong ball fourth, and
Figure 1.
Rolling race setup.
brian diskin
the metal socket last. Let’s try to make
sense of that. Does the heaviest object
win? Well, the golf ball is heavy, but
the metal socket is heavier, so clearly
the weight of the object isn’t what determines the finish order. How about
size? Nah. A medium-size object (the
golf ball) won, the smallest object
(the marble) came in second, and the
largest object (the tennis ball) came in
third. So if the weight and size aren’t
the determining factors, what is? To
understand the results, you need to
do a short activity.
Spin Your Friend
Find an office chair or a bar stool that
rotates. Also, find two small, heavy
objects and a friend (these are separate—you can’t count your friend
as a small, heavy object). Have your
friend (not a student) sit on the rotating chair and hold the heavy objects in
close to his or her body (switch places
if your friend doesn’t like spinning in a
circle). See the first drawing in Figure
2. Gently push on your friend to make
him or her spin. Note how difficult it
is to cause your friend to spin.
Now have your friend hold the
heavy weights out, with arms extended, as in the second drawing in
Figure 2. Again push to make your
friend spin, and again notice how difficult it is to cause him or her to spin.
What you should notice in this
activity is that it’s more difficult to
make your friend spin when the heavy
objects are extended than when they
are close to the body. That result is im-
Figure 2.
How difficult it is to make something spin depends not just on the mass of the object, but also on how the mass is
distributed in the object. The farther out from the center the mass is distributed, the more difficult it is to make the
object spin or rotate. Thus it is easier to spin a friend when their arms are close to the body.
brian diskin
October 2011 63
portant when dealing with objects that
are spinning in a circle. How difficult
it is to make something spin depends
not just on the mass of the object, but
also on how the mass is distributed in
the object. The farther out from the
center the mass is distributed, the
more difficult it is to make the object
spin or rotate. For those who want
official terms for things, the quantity
that tells you not just the mass of an
object but how it’s distributed is the
moment of inertia of the object.
The Force of Friction
All right, what does this have to do
with your race with rolling objects?
First, let’s discuss what would
happen in your race if the objects
slid down, without rolling, on an
extremely slick surface (Ideally,
this surface would be completely
frictionless). What would happen is that they would tie. Gravity is what’s causing them to slide
down the surface, and as I said
earlier, gravity is an equal opportunity accelerator. When objects
roll, however, the force of friction
is involved. That force of friction
causes the objects to roll. When
rolling is involved, you have to consider how difficult it is to cause the
objects to roll. The more difficult it
is to roll an object, the slower it will
be getting down the incline. And
from an energy perspective, you
not only have to provide energy for
the objects to get down the incline,
but you have to provide energy for
them to roll. The more energy that
goes into making the objects roll,
the less there is to get them moving
down the incline.
64 Science and Children
Let’s look at all the objects and
their distribution of mass. The golf
ball has a lot of mass concentrated at
the center (if you don’t believe me,
take a golf ball apart—you’ll find a
relatively small-mass covering, then
small-mass rubber bands, then a hard,
large-mass core). Therefore, it should
be relatively easy to make the golf ball
spin. The marble has its mass evenly
distributed throughout the marble.
The tennis ball, the Ping-Pong ball,
and the metal socket have their mass
distributed at the outside edges of the
objects, so they should be relatively
difficult to spin or roll. See Figure 3.
And this explains the result of our
race. The golf ball’s mass is concentrated near the center of the ball, so it
spins or rolls easier with a given applied force. Thus, the golf ball wins.
The socket, with lots of mass concentrated at its outer edge, loses the race.
The other objects place in the race
according to how much their mass
is concentrated toward the center or
toward the edge of each object.
Of course, this whole idea of things
being more or less difficult to spin
based on their mass distribution has
applications beyond objects rolling
down an incline. No doubt you’ve
Figure 3.
The distribution of an object’s mass determines
how easily it spins or rolls.
Ping-Pong ball
brian diskin
seen racing bicycles that have wheels
with a solid area where the spokes
normally are located. That results
in the mass of the wheel being closer
to the center of the wheel, so it spins
more easily. Ever wonder why figure
skaters spin much faster when they
pull their arms in? They’re bringing the mass of their body closer to
the center so they spin more easily.
Divers and gymnasts use this same
trick, curling their body up into a
ball in order to have it rotate more
easily. To try this for yourself, grab
that friend, the rotating chair, and
the heavy weights again. Have one
of you begin spinning on the chair,
slowly, with the weights extended.
Then pull the weights into your body.
Cool, no? Finally, many engines have
a “governor” on them that prevents
them from spinning too fast. There’s
a mechanism that moves weights out
away from the center of the engine as
the engine spins faster. That makes it
more difficult for the engine to spin,
and provides a “top speed” beyond
which the engine cannot go. And for
the nitpickers out there, many of the
examples I’ve given of rotating faster
by changing the distribution of mass
fall under the category of conservation
of angular momentum. At the basis of
that principle, though, is the simple
fact that it’s easier to cause something
to rotate when the mass is concentrated at the center of the object.
As an even more practical application for those of you who are parents,
you now have the key to helping your
kids make a faster soap box derby
car. Keep the mass of the wheels
near the center and thank physical
science concepts as your kids hit the
high speeds. n
Bill Robertson ([email protected]
com.com) is the author of the
NSTA Press book series, Stop Faking It! Finally Understanding Science So You Can Teach It.
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