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Gert
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Solve this by analogy with a translating body (not rotating). Its linear momentum $p$ is:

$$p=mv$$

With $m$ the mass and $v$ the linear velocity.

Take the derivative to time of both sides:

$$\frac{dp}{dt}=m\frac{dv}{dt}=ma=F$$

For a purely rotating body the angular momentum is $\vec{L}$:

$$\vec{L}=I\vec{\omega}$$

Where $\vec{\omega}$ is the angular velocity and $I$ the moment of inertia about the axis of rotation.

Take the derivative in time of both sides:

$$\frac{d\vec{L}}{dt}=I\frac{d\vec{\omega}}{dt}=\vec{\tau}$$ Where $\vec{\tau}$ is the torque vector required to effectuate a change in direction of the angular momentum vector $\vec{\omega}$.

In scalar notation we can write:

$$\tau=\alpha I$$

Where $\alpha$ is the rate of change of direction of the $\vec{\omega}$ vector in $\mathrm{radians/s}$. If you want the flywheel to change its plane of rotation only slowly then only a small torque is needed but faster changes require higher torque.

Gert
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