Force can exert over distance {energy}|. Energy is scalar, because motion component does not matter since force vector and distance vector have same direction. Net force can act over distance in direction {work, energy}. Forces can act over distances in all random directions {heat}. Heat has no net force. Forces must act for some time over some distance, so energy can exchange and motion can change.
Energy {kinetic energy}| can involve motion. Kinetic energy equals one-half times mass m times velocity v squared: KE = 0.5 * m * v^2. If object does work and loses speed, object loses kinetic energy. If object receives work and increases speed, object gains kinetic energy.
force
Collision, pushing, pulling, or other contact force F acting over distance ds makes mass m accelerate a to velocity v: dKE = F * ds = m * a * ds = m * (dv / dt) * ds = m * dv * ds / dt = m * v * dv, where t is time. Integral of dv = v/2, so KE = 0.5 * m * v^2.
comparison
Energy is either kinetic expressed energy or potential stored energy, because force times distance makes kinetic energy, and kinetic energy can act against force over distance to make potential energy.
Energy {potential energy}| can depend on force exerted over distance against field. Potential energy PE equals m times acceleration a times distance moved in field h: PE = m * a * h. If object moves to position with less force, object gains potential energy. If object moves to position with more force, object loses potential energy.
field
Field is gravitational, electric, or nuclear force field.
position
Potential energy depends on field force and object field position. If object moves farther away from attraction center, object gains potential energy. If object moves farther away from repulsion center, object loses potential energy. Small movements in strong fields can equal large movements in weak fields.
Exerted force can work against field force, and object gains potential energy. Field force can move object to do work, and object loses potential energy.
action
Going from one point to another point in potential field has only one path, with least average difference between kinetic and potential energy over time.
potential
Fields have measures {electric potential} {potential, electricity} of potential energy that depend on only source mass or charge, not on test-object mass or charge. Gravitational potential V is gravitational constant G times mass m at field center, divided by distance r from center: V = G * m / r. Electrical potential V is electric constant k times charge q at field center, divided by distance r from center: V = k * q / r.
Energy can flow per unit time {power, physics}|. Time t divides into energy E: P = (Ef - Ei) / (tf - ti). Power is constant force F times constant velocity v: P = F*v = F * (ds / dt) = (F * ds) / dt = dE / dt. Power is scalar, because energy is scalar.
Spinning or orbiting objects have rotation energy {rotational kinetic energy}. Because tangential velocity v equals angular velocity w times radius r, rotational kinetic energy KE equals half moment of inertia I times angular velocity w squared: KE = 0.5 * m * v^2 = 0.5 * m * (w*r)^2 = 0.5 * m * r^2 * w^2 = 0.5 * (m * r^2) * w^2 = 0.5 * I * w^2, where moment of inertia I = m * r^2.
work
Energy can be force over distance around axis {rotational work}. Rotational work W equals torque T times angle A in radians: W = F*s = (T/r) * (r*A) = T*A.
power
Energy can be force over time around axis {rotational power}. Rotational power P equals torque T times angular velocity w: P = E/t = (F*s) / t = ((T/r) * (r*A)) / t = T * (A/t)= T*w.
Force can act over distance in direction to transfer energy {work, physics}|. Net force F acts over distance change (sf - si) to perform work E: E = F * (sf - si). Small force Fs exerted over large distance sl can do same work as large force Fl exerted over short distance ss: Fs * sl = Fl * ss.
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Date Modified: 2022.0225