Areal velocity equal to the magnitude of the cross product of vectors "AB" and "AC". This area can also be viewed as a vector with this magnitude, pointing in a direction perpendicular to the parallelogram; this vector is the cross product itself: Hence The areal velocity is this vector area divided by Δ"t" in the limit that Δ"t" becomes vanishingly small: But, formula_4 is the velocity vector formula_5 of the moving particle, so that On the other hand, the angular momentum of the particle is and hence the angular momentum equals 2"m" times the areal velocity. Conservation of areal velocity is a
Wheelie to mass times acceleration, then the minimum power required for a wheelie can be expressed as the product of mass, velocity, and the minimum acceleration required for a wheelie: Thus the minimum power required is directly proportional to the mass of the vehicle and to its velocity. The slower a vehicle is moving, the less power is required to perform a wheelie, and that is without even considering the power required to overcome air drag, which increases with the cube of velocity. Therefore, the least amount of power required is when the vehicle begins accelerating from rest. In the case