Question

A locomotive is propelled by a turbine whose axle is parallel to the axes of wheels. The turbine's rotation direction coincides with that of wheels. The moment of inertia of the turbine rotor relative to its own axis is equal to $I=240kg\cdot m^2$. If the additional force exerted by the gyroscopic forces on the rails when the locomotive moves along a circle of radius $R=250m$ with velocity $v=50km/h$ is $F_{add}=\frac{x}{10}kN.m$, find the value of $x$. The gauge is equal to $l=1.5m$. The angular velocity of the turbine equals $n=1500rpm$.

Answer 1

A couple $\frac{2\pi Inv}{R}$ must come in play. This can be done if a force, $\frac{2\pi Inv}{Rl}$ acts on the rails in opposite directions in addition to the centrifugal and other forces. The force on the outer rail is increased and that on the inner rail decreased. The additional force in this case has the magnitude $1.4kN.m$