The Precessing Top

The Precessing Top - This equation shows that the change in...

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The Precessing Top Figure 12.12. The precessing top. A top, set spinning, will rotate slowly about the vertical axis. This motion is called precession. For any point on the rotation axis of the top, the position vector is parallel to the angular momentum vector. The weight of the top exerts an external torque about the origin (the coordinate system is defined such that the origin coincides with the contact point of the top on the floor, see Figure 12.12). The magnitude of this torque is The direction of the torque is perpendicular to the position vector and to the force. This also implies that the torque is perpendicular to the angular momentum of the spinning top. The external torque causes a change in the angular momentum of the system
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Unformatted text preview: This equation shows that the change in the angular momentum dL that occurs in a time dt must point in the same direction as the torque vector. Since the torque is at right angle to L, it can not change the magnitude of L, but it can change its direction. The result is a rotation of the angular momentum vector around the z-axis. The precession angle d[phi] is related to the change in the angular momentum of the system: This shows that the precession velocity is equal to This equation shows that the faster the top spins the slower it precesses. In addition, the precession is zero if g = 0 m/s 2 and the precession is independent of the angle [theta]....
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