Activity: Rotational Inertia
Objectives: To develop a better understanding of the factors affecting rotational inertia
Inertia is a measure of how much an object resists changes in motion. For linear motion, the
inertia is the mass; the greater the mass, the harder it is to accelerate an object as seen in
Newton=s 2nd law
F = ma
or
a = F/m.
You can Afeel@ the inertial mass (as opposed to gravitational mass) of an object by quickly
moving it back and forth horizontally. This motion involves continuous acceleration, and thus
the continuous exertion of force. The greater the mass, the harder it will be to move the object.
Try it with two masses, the 100 gram mass and the 500 gram mass. (Or take a cart without the
additional mass and then with the additional mass.) Oscillate them back and forth horizontally
with just your fingers. Which is harder?
Rotational inertia is similarly defined. It is a measure of how much an object resists changes in
rotation, i.e. rotational acceleration. You can Afeel@ the rotational inertia of an object by quickly
rotating the object back and forth with just your fingers (or your hand if its heavier). This motion
involves continuous rotational acceleration, and thus the continuous exertion of torque. The
greater the moment of inertia, the harder it will be to oscillate the object. We will explore how
mass and mass distribution affect the moment of inertia.
Experiment A: Moment of inertial vs. mass
1. Take out your rotary motion kit. You should have two rods of the same length, one solid
and one hollow (remove the weights from the hollow rod).
a. Which is heavier, the solid rod or the hollow rod?
b. Which do you expect to have the greater moment of inertia?
c. Oscillate the two rods with your fingers about the middle. Which is harder? Which
has the greater moment of inertia, the heavy rod or the light rod?
2. Write out a statement as to how mass affects moment of inertia.
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Experiment B: Moment of inertia vs. mass location
1. Put the two weights on the hollow rod equidistant from the center near the ends.
Oscillate the rod about the middle with your fingers. Note the difficulty.
2. Move the two weights about half way toward the middle (still equidistant from the
center). Oscillate the rod about the middle with your fingers.
3. Move the weights as close to center as possible, leaving room for your fingers. Oscillate
the rod about the middle with your fingers.
4. Rank the moment of inertia of the rod/weight combination from largest to smallest.
5. Write out a statement as to how mass distribution affects moment of inertia.
Experiment C: Moment of inertia vs. axis location
1. Take the solid rod without any masses attached. Where is the center of mass?
2. Oscillate the rod with your fingers at the center of mass. Note the difficulty.
3. Now hold the rod near the end and oscillate it. Is it harder or easier than about the center
of mass? About which axis location is the moment of inertia smaller?
3. Oscillate the rod about various points along its length. Which point is easiest?
4. Write out a summary statement about how moving the location of the axis of rotation
affects the moment of inertia
Exercises
1. Suppose you are designing a rotor that you want to start rotating as easily as possible.
Would you want the mass concentrated near the center or near the outside?
2. Suppose you are designing a rotor that you want to be hard to stop. Would you want the
mass concentrated near the center or near the outside?
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