Probelm2 answer with details plz: As a motorcyclist drives around a flat circula

Question

Probelm2 answer with details plz:

As a motorcyclist drives around a flat circular curve, he must lean into the turn. For a given turn radius, the speed of travel dictates how much lean is required. When the cyclist is upright his center of mass is a distance h above horizontal ground. Define the tip angle, psi, to be the angle between vertical and the line joining the cyclist's center of mass and the ground. Show that the tip angle psi must satisfy the equation tan psi = v2/gR where v is the linear speed of the cyclist around the flat curve of radius R. The acceleration due to gravity is g. Note: You will need to take a horizontal axis of rotation through the center of mass so that you may ignore any 'centrifugal' effects associated with being in an accelerated reference frame.

Explanation / Answer

to calculate the leaning angle

we need to balance the moment of wieght and centrifugal force

(mv^2/R)*L*cos(theta)=mg*L*sin(theta)

==> tan(theta)=v^2/Rg

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