Physics 105, Fall Term, 2009

Reading: Chapter 8.5-8.6

Did you complete the reading assignment?

Yes No

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.

Exercise 1

Return to: 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 rotating slowly.

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 inertia?

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 first?

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

Exercise 2

Now go to: http://canu.ucalgary.ca/map/content/energy/energy_cons/simulate/race/applet.html. 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?

Disk Hoop Sphere

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.

Go to: 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 I_{z} 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 fastest?

The sphere gets to the bottom first because it has the lowest moment of inertia; therefore, it takes the least energy to rotate it.

The comments entered in these last two boxes go into a big anonymous data file that I will use to guide the lectures of the day. That means two things:

1) If you have a specific question or concern and would like an individual answer you will need to come by the office or send an email. 2) If you really want to get an anonymous comment to me before the lecture, it must be submitted before 11am that day.

Was there anything that you didn't understand in the reading assignment? What was confusing to you?

General Comments: