03 Maximum Rotational Inertia

Aim¶

To show that an object prefers to rotate around an axis with largest moment of inertia.

Subjects¶

• 1Q10 (Momentum of Inertia)

• 1Q60 (Rotational Stability)

Diagram¶

Equipment¶

• Electric hand drill (or other electric motor).

• Aluminium bar $\varnothing 12 \mathrm{~mm}, l=180 \mathrm{~mm}$ with string $l=200 \mathrm{~mm}$.

• A rope, $l=500 \mathrm{~mm}$.

• A chain, $l=500 \mathrm{~mm}$.

• Transparent screen

Presentation¶

The bar hung from a string is fixed to the drill and set spinning. The bar starts to rotate and will not remain vertical, but rises. Finally, the bar spins in a horizontal plane (see Diagram).

A rope suspended in the drills head will climb very fast to a rotation in a horizontal plane (passing through an interesting sequence of movement).

When a chain is used, this chain will also finally rotate in a horizontal plane, but it takes much more time to go from the vertical suspension to the horizontal rotation. (Now a study of the sequence in between is possible.)

Figure 2 shows several objects that can be used in this demonstration.

Explanation¶

• When the vertical bar is just a little out of its equilibrium, then due to opposing centripetal forces on the upper and lower part of the bar, the bar will eventually align itself horizontally.

• The angular velocity vector $\omega$ points vertically downward. The angular vector momentum does not, because the rotational inertia of the bar is greater about an axis perpendicular to the bar. The downward impulse $\vec{L} \Delta t$ attempts to align the angular momentum with $\omega$.

Remarks¶

• While rotating the bar, rope or chain, take care that these objects, while rotating horizontally, leave enough free space. A transparent screen between the rotating objects and the observers is advised.

Sources¶

• Meiners, Harry F., Physics demonstration experiments, part I, pag. 275

• Roest, R., Inleiding Mechanica, pag. 216-222