Question 3

An ant crawls with constant speed $v$ outward along a spoke of a wheel which is rotating with constant angular velocity $\omega$ about a vertical axis. Show that, when the ant is at a distance $r$ from the centre of the wheel, the minimal frictional force needed to keep the ant moving in this way has a magnitude

$$F = \sqrt{ (2m\omega v)^2 + (m\omega^2 r)^2 }.$$

[Hints can be found here, but do not follow this link until you have attempted the question on your own.]