(a) A flying disc (frisbee) is modelled as a uniform thin flat disc of radius , so…

PHYSICS · Subjective · Fermi University Physics · Mechanics & Dynamical Systems · Rotation, rigid bodies and accelerated frames · Rotation, rigid bodies and accelerated frames

Action and Symmetry, Ch Euler's equations, free precession and the heavy symmetric top

Problem

(a) A flying disc (frisbee) is modelled as a uniform thin flat disc of radius

0.135\,\mathrm{m}

, so that

I_3=\tfrac12MR^2

about its spin axis and

I_1=\tfrac14MR^2

about a diameter. Thrown spinning at

7.0

revolutions per second with a slight wobble and no further torque, estimate the rate (in revolutions per second) at which

\boldsymbol\omega

circles the disc's symmetry axis, as seen by a tiny observer riding on the disc. (b) A laboratory demonstration gyroscope has a flywheel of mass

0.30\,\mathrm{kg}

and radius

5.0\,\mathrm{cm}

, mounted with its centre

6.0\,\mathrm{cm}

from the pivot. Using

I_3=\tfrac12MR^2

and

I_1=\tfrac14MR^2+Md^2

(parallel-axis rule, treating the mount as light), it is spun up to

3000

revolutions per minute and released spinning upright. A constant bearing-and-air friction torque of

1.0\times10^{-3}\,\mathrm{N\,m}

slows the spin. Taking

g=9.8\,\mathrm{m\,s^{-2}}

, estimate the spin rate at which it stops sleeping and the time after release at which that happens.

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