Real and Pseudo Forces

Consider standing inside a lift (elevator). When the lift starts moving UPWARD (accelerating upward), you feel heavier, as though someone is pushing you down -- and this is not imaginary: a weighing scale under your feet genuinely records an increased reading during this phase. During travel at constant velocity, no such extra force is felt or recorded. When the lift decelerates while stopping at a floor above (i.e. accelerates downward), the scale records a DECREASE in weight, and you feel lighter.

These extra apparent forces have three defining characteristics: (i) they are MEASURABLE (with a genuine instrument, like a weighing scale) -- not merely imagined; (ii) they are NOT accounted for by Newton's second law when analysed from an INERTIAL frame; (iii) they are not any of the four fundamental forces. Because they satisfy neither of the conditions that define a 'real' force (obeying Newton's laws, and being one of the four fundamental forces), they are called PSEUDO forces -- 'pseudo' here means 'non-real', not 'imaginary' (much as, in mathematics, a 'non-real' complex number is nonetheless not literally imaginary or fictitious in the everyday sense).

Pseudo forces are always measured to have magnitude $-m\vec{a}$, where $\vec{a}$ is the acceleration of the (non-inertial) reference frame itself and m is the mass of the object experiencing the pseudo force; adding this pseudo force to the resultant of all real forces lets Newton's second law be applied consistently even inside an accelerating frame. The negative sign shows the pseudo force always points OPPOSITE to the frame's acceleration.

Applying this to the lift: with downward acceleration $\vec{a}$, the apparent weight is $W'=mg-ma$ (loss of weight, since $\vec{g}$ and $\vec{a}$ point the same way here); with upward acceleration $a_1$, the apparent weight is $W'=mg+ma_1$ (gain in weight, since $\vec{g}$ and $\vec{a_1}$ are now oppositely directed). …