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
Power (physics) yields: where "A" and "B" are the beginning and end of the path along which the work was done. The power at any point along the curve "C" is the time derivative In one dimension, this can be simplified to: In rotational systems, power is the product of the torque τ and angular velocity ω, where ω measured in radians per second. The formula_13 represents scalar product. In fluid power systems such as hydraulic actuators, power is given by where "p" is pressure in pascals, or N/m and "Q" is volumetric flow rate in m/s in SI units. If a