Alternative Exercise 10.145 A Falling Bicycle. The moment of inertia of the fron

Question

Alternative Exercise 10.145

A Falling Bicycle. The moment of inertia of the front wheel of a bicycle about its axle is I, its radius is r, and the forward speed of the bicycle is v.

With what angular velocity must the front wheel be turned about a vertical axis to counteract the capsizing torque due to a mass m located a distance x horizontally to the right or left of the line of contact of wheels and ground? (Bicycle riders: Compare your own experience and decide whether your answer seems reasonable.)

Take the free fall acceleration to be g.

Explanation / Answer

from the given data:

moment of inertia =I

radius = r

speed = v

acceleration due to gravity = g

angular velocity

' = mgx / I
where = v/r, so
' = mgxr / Iv

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