Physics 12

A frame of reference is the vantage point — a coordinate system attached to some object — from which you measure position, velocity, and time. Every measurement of motion is measurement relative to a chosen frame.

Postulate 1: the laws of physics are identical in every inertial reference frame — no experiment done inside a closed lab can tell you your frame's constant velocity.

A physical relationship can be linear ($y = mx + b$), exponential, or inverse (e.g. an inverse-square field law, $F \propto \frac{1}{r^2}$) — the SHAPE of the plotted data tells you which one you are looking at.

A frame is "inertial" if it is not accelerating; the laws of mechanics look the same in every inertial frame, which is why you cannot feel your own frame's constant-velocity motion from inside it.

Postulate 2: the speed of light in a vacuum, $c = 3.00 \times 10^8\ \text{m/s}$, is the same for every observer, no matter how the source or the observer is moving.

An object in translational static equilibrium has zero net force: $\sum \vec{F} = 0$, which must hold separately in the vertical direction AND the horizontal direction.

Uniform circular motion requires a net force pointing toward the centre: $F_c = \frac{mv^2}{r}$, producing centripetal acceleration $a_c = \frac{v^2}{r}$ — speed stays constant but direction (hence velocity) constantly changes.

A salmon wheel uses the force of flowing river current on angled paddles to rotate baskets that scoop migrating fish — a continuous energy-and-force system engineered entirely from water flow, with no motor.

Solving means resolving every force (weight, tension, normal, applied) into $x$- and $y$-components, then setting each direction's sum to zero and solving for the unknowns.

The centripetal force is not a NEW kind of force — it is whatever real force (tension, gravity, friction, normal force) happens to point toward the centre and supply the required $\frac{mv^2}{r}$.

Every mass creates a gravitational field — a vector field filling the space around it that exerts a force on any other mass placed within it, weakening with distance.

Gravitational potential energy between two masses is $E_p = -\frac{Gm_1m_2}{r}$ — the ENERGY stored by their separation within each other's field, with the zero point chosen at infinite separation.

For a circular orbit, gravity SUPPLIES the centripetal force: $\frac{Gm_1m_2}{r^2}$$= \frac{m_2v^2}{r}$, which solves for orbital speed $v = \sqrt{\frac{Gm_1}{r}}$ — independent of the orbiting object's own mass.

Every charge creates an electric field in the surrounding space — the field exerts a force on any other charge placed within it, pointing away from a positive source charge and toward a negative one, and can attract or repel.

Electric potential ENERGY ($E_p$, in joules) belongs to a PAIR of charges — the energy stored by their position relative to each other as work is done to assemble them within each other's field.

Momentum is a vector, $\vec{p} = m\vec{v}$, measured in $\text{kg·m/s}$ — mass in motion, with direction mattering as much as size.

In an isolated system, total momentum before a one-dimensional collision equals total momentum after: $\sum p_i = \sum p_f$ — this holds in EVERY collision, no exceptions.

Impulse is force applied over time, $\vec{J} = \vec{F}\Delta t$, and it equals the resulting change in momentum, $\vec{J} = \Delta \vec{p}$ — for a fixed $\Delta p$, a longer contact time means a smaller average force (the physics behind airbags and crumple zones).

Kinetic energy is conserved ONLY in a perfectly elastic collision. In an inelastic collision some kinetic energy converts to heat, sound, or deformation; a completely inelastic collision (objects stick together and move with one common final velocity) loses the most.

In a two-dimensional collision among multiple objects, momentum is conserved separately in the $x$-direction and the $y$-direction: resolve each velocity into components before applying $\sum p_{x,i} = \sum p_{x,f}$ and $\sum p_{y,i} = \sum p_{y,f}$.

The number of significant figures in a measured quantity reflects how precisely it was actually measured; a calculated result can never be MORE precise than its least-precise input.

When a derived quantity (like a calculated field strength, force, or relativistic quantity) is built from several measured values, the uncertainty in each measurement carries through into the uncertainty of the final result — the derived value is only as reliable as its least certain input.

In a multi-step calculation — like combining several measured values in an inverse-square field formula, or computing $\gamma$ then using it in a time-dilation or length-contraction expression — carry extra guard digits through the intermediate steps and round only the FINAL answer to the correct number of significant figures.

Scientific notation ($a \times 10^n$, with $1 \leq a < 10$) makes very large or very small results (like $6.67 \times 10^{-11}$ or $5.97 \times 10^{24}$) readable and keeps the correct number of significant figures unambiguous.