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#
Fig. 191 .#
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 192 shows several objects that can be used in this demonstration.
Fig. 192 .#
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