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Dynamics of a solid body

Problem 1.284

A gyroscope, a uniform disc of radius R=5.0 cmR=5.0 \mathrm{~cm} at the end of a rod of length l=10 cml=10 \mathrm{~cm} (Fig. 1.73),), is mounted on the floor of an elevator car going up with a constant acceleration w=2.0 m/s2.w=2.0 \mathrm{~m} / \mathrm{s}^{2} . The other end of the rod is hinged at the point O.O . The gyroscope precesses with an angular velocity n=0.5n=0.5 rps. Neglecting the friction and the mass of the rod, find the proper angular velocity of the disc.

Reveal Answer
 1.284. ω=(g+w)l/πnR2=3××102rad/s\begin{array}{l} \text { 1.284. } \omega=(g+w) l / \pi n R^{2}=3 \times \\ \times 10^{2} \mathrm{rad} / \mathrm{s} \end{array}
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