Variable-mass system events. The following derivation is for a body that is gaining mass (accretion). A body of time-varying mass "m" moves at a velocity v at an initial time "t". In the same instant, a particle of mass dm moves with velocity u. The initial momentum can be written as Now at a time "t" + d"t", let both the main body and the particle accrete into a body of velocity v + dv. Thus the new momentum of the system can be written as Since d"m"dv is the product of two small values, it can be ignored, meaning during d"t"
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