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Spinning Disk Pendulum Swinging on Top of a Rotating Table.
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Lecture_05 - spinning top equation of motion. In this lecture, you use the parallel axis theorem to change the point of rotation for a 3D object. Kinetic energy, $ T $, can be written in 3 ways for a rigid body: T = 1 2 m v G 2 + 1 2 ω H G. T = 1 2 ω H B. T = 1 2 m v B 2 + 1 2 m v B ⋅ v G + 1 2 ω H B. where.

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PDF Chapter 11 Angular Momentum; General Rotation.

To explain this mathematically consider a spinning top on earth with angular velocity ω its angular velocity of precession ω p and angle of precession as ϕ. its angular momentum is defined as: L → = ω → I. Say spinning top rotated Δ θ and its change in angular momentum is Δ L. Then we can express Δ θ as following.

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Figure 1. (color online) Precession of a heavy symmetric top. (A) focuses on angular frequencies, while (B) on angular momenta. The index lab specifies the axis of the laboratory (inertial) reference frame. Quantities associated with precession are marked by p, those with spinning by s, and the ones related to the symmetry axis and the principal axes perpendicular to it, by n and ⊥. Gyroscopic precession is a cyclic process, whereas a spinning top falling over is an irreversible event. In the absence of friction a torque cannot topple a spinning top all the way down. Presence of a torque (exerted on a spinning top) can lead to a state of gyroscopic precession, but it cannot lead to the top toppling over all the way to the.

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This Demonstration shows a pendulum with a small spinning rigid cylindrical bob in which the pendulum rod (assumed to have negligible mass) swings from a frame fixed on top of a rotating table. The system has three degrees of freedom: the pendulum swing angle , the spin angle of the pendulum bob, and the rotation angle of the large table.