A cylindrical disc of a gyroscope of mass m=15kg and radius r=5.0cm spins with an angular velocity omega=330rad//s. The distance between the bearings in which the axle of the disc is mounted is equal to l=15cm. The axle is forced to oscillate about a horizontal axis with a period T=1.0s and amplitude varphi_m=20^@. Find the maximum value of the gyropscopic forces exerted by the axle on the bearings.

A cylindrical disc of a gyroscope of mass m=15kg and radius r=5.0cm sp

1.	A cylindrical disc of a gyroscope of mass m=15kg and radius r=5.0cm spins with an angular velocity omega=330rad//s. The distance between the bearings in which the axle of the disc is mounted is equal to l=15cm. The axle is forced to oscillate about a horizontal axis with a period T=1.0s and amplitude varphi_m=20^@. Find the maximum value of the gyropscopic forces exerted by the axle on the bearings.
Answer» <html><body><p></p>Solution :The <a href="https://interviewquestions.tuteehub.com/tag/moment-25786" style="font-weight:bold;" target="_blank" title="Click to know more about MOMENT">MOMENT</a> of inertia is `1/2mr^2` and angular momentum is `1/2mr^2omega`. The axis oscillates about a horizontal axis making an <a href="https://interviewquestions.tuteehub.com/tag/instantaneous-516608" style="font-weight:bold;" target="_blank" title="Click to know more about INSTANTANEOUS">INSTANTANEOUS</a> <a href="https://interviewquestions.tuteehub.com/tag/angle-875388" style="font-weight:bold;" target="_blank" title="Click to know more about ANGLE">ANGLE</a>. <br/> `varphi=varphi_m"sin"(2pit)/(T)` <br/> This <a href="https://interviewquestions.tuteehub.com/tag/means-1091780" style="font-weight:bold;" target="_blank" title="Click to know more about MEANS">MEANS</a> that there is a variable precession with a rate of precession `(dvarphi)/(dt)`. The <a href="https://interviewquestions.tuteehub.com/tag/maximum-556915" style="font-weight:bold;" target="_blank" title="Click to know more about MAXIMUM">MAXIMUM</a> value of this is `(2pivarphi_m)/(T)`. When the angle between the axle and the axis is at the maximum value, a torque `IomegaOmega` <br/> `=1/2mr^2omega(2pivarphi_m)/(T)=(pimr^2omegavarphi_m)/(T)` acts on it. <br/> The corresponding gyroscopic force will be `(pimr^2omegavarphi_m)/(lT)=90N`</body></html>

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