Physics 105, Fall Term, 2009
Did you complete the reading assignment?
1) The greater the
moment of inertia, the more difficult it is to change its rotational motion.
2) Rotating objects use energy to
rotate. This energy is called rotational kinetic energy.
Moment of inertia is basically the rotational version of mass. Just as it
takes more effort to move a larger mass, it takes more effort to rotate an
object with a larger moment of inertia. Just as a small mass will accelerate
more quickly than a large mass when the same force is applied to each, an
object with a small moment of inertia will rotate more quickly than an
object with a large moment of inertia when the same torque is applied to
each. Moment of inertia only becomes difficult to understand when you lose
sight of the fact that like all rotational motion, it is the exact same as
its linear motion counterpart with a slightly different equation.
http://phet.colorado.edu/sims/rotation/torque_en.jnlp and click on the
tab that is labeled 'Moment of Inertia' at the top of the applet. In this
applet you can now change the size of the rotating platform with the top
three controls under the image of the platform. The only graph that you need
to pay attention to is the middle graph labeled 'Moment of Inertia'. The
'Reset All' button at the bottom left of the applet is also helpful if the
rotating platform disappears on you.
Apply a small force to the rotating platform for a short moment by clicking
on the platform and dragging the mouse slowly in a straight line in the
direction you want the platform to begin rotating and then release the
mouse. To be able to see the affects well you will need the platform to be
With the platform rotating quickly increase the inner radius of the platform
using the appropriate scrollbar. What affect did this have on the moment of
Increases moment of inertia
Decreases moment of inertia
Moment of inertia stays the same
What affect did this have on the angular velocity of the ladybug on the
platform? (There is no graph for angular velocity, you'll have to look at
this one physically)
Increases angular velocity
Decreases angular velocity
Angular velocity stays the same
Change the inner radius back to zero. Now quickly decrease the outer radius
of the platform using the appropriate scrollbar. What affect did this have
on the moment of inertia?
Change the outer radius back to 4 mm. Now quickly increase the mass of the
platform using the appropriate scrollbar. What affect did this have on the
moment of inertia?
If you were pushing your friend down Y Mountain in a garbage can and raced
it against an empty garbage can of identical size, and equal mass of your
friend and the other garbage can, which garbage can would get to the bottom
The empty garbage can
The garbage can with your friend in it
Both garbage cans will reach the bottom at
the same time.
Where should the mass of an object be in order for it to rotate quickly?
Near the axis of rotation
Far from the axis of rotation
Now go to:
Select the 'Friction' checkbox for both tracks. You can select which
objects you want to race by clicking on the specific object under the track
and race objects down the ramps when both ramps have an object selected by
pressing the 'Play' button. To race another set of objects, you will need to
click the 'Rewind' button before selecting new objects. Each object begins
with 64 J of gravitational potential energy, you can see how much linear
kinetic and rotational kinetic energy the objects have at the end of ramp by
watching the values located above the ramps (The TK stands for Translational
Kinetic energy, which is another term for linear kinetic energy).
Race each of the objects against each other (excluding the block). Which
objects gets to the bottom the fastest?
Do the masses of the objects have an effect on how fast the objects get to
the bottom? Why or why not?
No, mass does not effect how fast the objects get to the bottom. This is because the mass that is part of the linear and rotational kinetic energies is also a part of the gravitational potential energy, and the mass from each of these terms cancels out.
In terms of types of kinetic energy, why does the winning object get to the
bottom the fastest?
It takes the least amount of rotational kinetic energy to roll, leaving more linear kinetic energy as it approaches the bottom, giivng it a higher velocity.
http://en.wikipedia.org/wiki/List_of_moments_of_inertia and look at the
different moment of inertia for each of the objects that were raced (Only Iz
matters because the z-axis is the axis where the rotation occurs). Why in
terms of moment of inertia did the winning object get to the bottom the
The sphere gets to the bottom first because it has the lowest moment of inertia; therefore, it takes the least energy to rotate it.
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Was there anything that you didn't understand in the reading assignment?
What was confusing to you?