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Advanced dynamics of a spinning disk

The disk spins about its own axis at 1,200 rev/min as the system rotates about the vertical axis at 20 rev/min. Determine the angular velocity and angular acceleration of the disk if beta is constant at 30 degrees.

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Answer:
Angular Velocity:
The disk has two angular velocities,
(1) about its own axis, passing through its center
and (2) about the axis at a distance r = L+Lcos 

Spinning frequency of the disc n1 = 1200 rev/min i.e. rpm
= 1200/60 = 20 rev/sec (rps)
The angular speed of the disc about its own axis is 1 = 2n1 = 2x 3.14 x 20 = 125.6 rad/s.
As seen with the right hand rule, the direction of this angular velocity is perpendicular to the plane of the disc, directed from point O' to Q as represented by vector in figures 1 & 2.

Frequency of revolution of the disc about the axis OP n2 = 20 rev/min = 0.33 rev/s
The angular speed of the disc about axis OP 2 = 2n2 = 2x 3.14 x 0.33 = 2.0724 rad/s.
As seen with the ...

Solution Summary

The solution shows how to calculate the angular velocity and acceleration of a spinning and rotating disk.

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