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The position center of gravity of a bicycle and its rider is known, and the distance from it to the point of contact of the front wheel with the ground, in terms of horizontal and vertical distance (x cm and y cm), are both known, as well as the total weight of the bike and the rider. The brakes are then applied, making the bike turn around the point of contact with the ground of the front wheel, and this force is also known.

Is there a way to calculate the amount of torque generated from this information?

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The answer is no, as you don't know the moment of inertia, and changes te situation a lot: suppose the distribution of mass is that such that all mass is concentrated in the extreme points, and another case in which is uniformly distributed along the longitude: both cases generate the same center of mass and distances, but the torque will be different as mass distribution is different.

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