powerandforce

Power and force are fundamental concepts in physics that describe different aspects of motion and energy. Force is an interaction that can cause an object to accelerate, and it is measured in newtons. Power, by contrast, is the rate at which work is done or energy is transferred, and it is measured in watts.

The instantaneous power delivered by a force F acting on an object moving with velocity v is P = F · v, the dot product of force and velocity. If the force is in the same direction as the motion, P = F v. If opposite, P is negative. If the force is perpendicular to the motion, P = 0. The work W done by a force along a path is W = ∫ F · dx, and the work-energy theorem states that W equals the change in the object's kinetic energy (ΔK). Average power over a time interval equals that work divided by the interval, W/Δt.

In rotational motion, power is expressed as P = τ ω, where τ is torque and ω is angular velocity. In electrical contexts, power is often written as P = VI, with V the voltage and I the current; for resistive elements, P = I^2R or P = V^2/R.

Key distinctions: power is not energy itself but the rate of energy transfer. A device can have high power yet store little total energy. Understanding both concepts and their relationship via work and energy clarifies many physical situations, from engines and machines to simple push-and-motion problems. See also work, energy, torque, and efficiency.