» Maxwell spinner (0660)
Immagini
DESCRIPTION
Exhibit 660 is a Maxwell inertial top mounted on a rectangular metallic base with four rubber feet. It consists of a steel disk suspended by two strings attached to the ends of the axis of the disk. The disk can be raised by rotating its axis which winds up the strings. When released the disk converts gravitational potential energy into translational and rotational kinetic energy which begins to return to potential when the strings are fully unwound. In modern language this top behaves as a "yoyo"
If the disk falls from height S, the potential energy=m g S, where m is the mass of the disk is converted to kinetic energy of motion and of rotation. If ω is the angular velocity falling the distance S, the kinetic energy of rotation is ![Formula: [ \frac{1}{2} I\omega^2]](/foto/equaz/660_fr01.png "Formula: [ \frac{1}{2} I\omega^2]")
, where I is the moment of inertia of the disk around its axis normal to its plane of symmetry. The kinetic energy of translation is ![Formula: [\frac{1}{2}mv^2 ]](/foto/equaz/660_fr02.png "Formula: [\frac{1}{2}mv^2 ]")
where v is the final linear velocity. Thus
![Equazione: [ mgS = \frac{1}{2} I\omega^2+\frac{1}{2}mv^2 ]](/foto/equaz/660_eq01.png "Equazione: [ mgS = \frac{1}{2} I\omega^2+\frac{1}{2}mv^2 ]")
Since:
![Equazione: [ \omega^2 = \frac{v^2}{r^2} ]](/foto/equaz/660_eq02.png "Equazione: [ \omega^2 = \frac{v^2}{r^2} ]")
where r is the radius of the disk
Thus![Equazione: [ mgS = \frac{1}{2} I\frac{v^2}{r^2} + \frac{1}{2}mv^2 ]](/foto/equaz/660_eq03.png "Equazione: [ mgS = \frac{1}{2} I\frac{v^2}{r^2} + \frac{1}{2}mv^2 ]")
or also
![Equazione: [\frac{1}{2} I\frac{v^2}{r^2} = mg S - \frac{1}{2}mv^2]](/foto/equaz/660_eq04.png "Equazione: [\frac{1}{2} I\frac{v^2}{r^2} = mg S - \frac{1}{2}mv^2]")
The average velocity of fall;
![Formula: [ v_m = \frac{S}{t}]](/foto/equaz/660_fr03.png "Formula: [ v_m = \frac{S}{t}]")
,
where t is the fall time through distance S, thus the final velocity is
![Formula: [ v = \frac{2S}{t}]](/foto/equaz/660_fr04.png "Formula: [ v = \frac{2S}{t}]")
, and ![Formula: [ v^2 = \frac{4S^2}{t^2} ]](/foto/equaz/660_fr05.png "Formula: [ v^2 = \frac{4S^2}{t^2} ]")
From this relation one can derive the moment of inertia of the disk:
D
![Equazione: [ I = mr^2\bigg(\frac{gt^2}{2S} -1\bigg )]](/foto/equaz/660_eq05.png "Equazione: [ I = mr^2\bigg(\frac{gt^2}{2S} -1\bigg )]")
BIBLIOGRAPHY
- [1] MATHUR, D. S. Elements of Properties of Matter. S. Chand CO., 1959.
Dati Catalografici
| Data di costruzione: | --- |
|---|---|
| Data di carico: | Ignota |
| Nr. Inventario: | Ignoto (Ignoto) |
| Costruttore: | Costruttore sconosciuto |
| Materiale: | acciaio, metallo, gomma |
| Dimensioni: | Base: 28 cm x 15 cm x 2,5 cm; Altezza totale: 37 cm; Diametro del disco: 10 cm; Lunghezza dei fili: 20 cm; lunghezza dell'asse: 4 cm |
| Conservazione: | buono |