Explore BrainMass

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.

See attached file for full problem description.


Solution Preview

Now please see the solution to your problem in the attached word file

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.