A gyroscope has \(L=6.0\,\mathrm{kg\,m^2\,s^{-1}}\) and experiences torque \(1.5\,\mathrm{N\,m}\) perpendicular to \(\vec L\). Find the slow precession rate.

A rotor has \(I_s=0.020\,\mathrm{kg\,m^2}\) and \(\omega_s=400\,\mathrm{rad\,s^{-1}}\). Find its spin angular momentum.

If the spin angular speed of a gyroscope is doubled while the gravitational torque is unchanged, what happens to the slow precession rate?

A gyroscope's centre of mass is directly below its pivot. What gravitational torque acts about the pivot?

A gyroscope has \(M=1.2\,\mathrm{kg}\), \(d=0.15\,\mathrm{m}\), \(I_s=0.030\,\mathrm{kg\,m^2}\), and \(\omega_s=250\,\mathrm{rad\,s^{-1}}\). Find \(\Omega\).

A precessing gyroscope has \(\tau=0.80\,\mathrm{N\,m}\) and \(\Omega=0.20\,\mathrm{rad\,s^{-1}}\). Find \(L\).

A \(2.0\,\mathrm{kg}\) gyroscope has its centre of mass \(0.10\,\mathrm{m}\) from the pivot and precesses at \(0.50\,\mathrm{rad\,s^{-1}}\). Find the required spin angular momentum.

A rotor with \(I_s=0.015\,\mathrm{kg\,m^2}\) must have \(L=9.0\,\mathrm{kg\,m^2\,s^{-1}}\). Find the required spin rate in \(\mathrm{rad\,s^{-1}}\) and revolutions per second.

A gyroscope has \(I_s=0.040\,\mathrm{kg\,m^2}\), \(\omega_s=300\,\mathrm{rad\,s^{-1}}\), \(M=2.0\,\mathrm{kg}\), and \(d=0.12\,\mathrm{m}\). Find \(\Omega\) and check whether \(\Omega\ll\omega_s\).

A gyroscope must precess no faster than \(\Omega_{\max}\). Derive the minimum spin speed \(\omega_s\) in terms of \(M\), \(g\), \(d\), \(I_s\), and \(\Omega_{\max}\). State the slow-precession check.

Starting from \(\vec\tau=d\vec L/dt\), derive the slow-precession formula \(\Omega=\tau/L\) for a gyroscope whose torque is perpendicular to its spin angular momentum. State the assumptions in the derivation.

A gyroscope has spin inertia \(I_s\), initial spin \(\omega_0\), mass \(M\), lever arm \(d\), and bearing drag torque \(c\omega_s\) opposing the spin. Using the slow-precession approximation, derive \(\omega_s(t)\), \(\Omega(t)\), and the time at which \(\Omega\) first reaches a limit \(\Omega_{\max}\), including the condition that this failure time exists.