Physics 11

A scalar has magnitude only — distance, speed, time, mass, energy. A vector has magnitude AND direction — displacement, velocity, acceleration, force.

Any vector at an angle can be split into an x-component and a y-component: $F_x = F\cos\theta$ and $F_y = F\sin\theta$, where $\theta$ is measured from the x-axis.

Uniform motion means constant velocity (zero acceleration): $v = \frac{d}{t}$.

A vertically launched or dropped object undergoes uniformly accelerated motion with $a = g = 9.81\ \text{m/s}^2$ downward — the same kinematics equations apply as for horizontal motion, just along the vertical axis.

Horizontal motion during a projectile's flight is uniform (constant velocity, no horizontal force if air resistance is ignored): $d_x = v_x t$.

Contact forces require touching surfaces: the normal force (perpendicular to the surface, supports weight), friction (parallel to the surface, opposes relative sliding), spring force, and tension force.

Mass is the amount of matter in an object (kg) — it does not change with location. Weight is the force of gravity on that mass, $F_g = mg$, and DOES change with the local gravitational field.

Newton's 1st law (inertia): an object at rest stays at rest, and an object in motion stays in motion at constant velocity, in a straight line, unless acted on by a net (unbalanced) force.

A free-body diagram shows ONLY the forces acting ON the object of interest (not forces it exerts on other things), each drawn as an arrow from a single point representing the object.

Balanced forces sum to a net force of zero — the object is at rest or moving at constant velocity (Newton's 1st law). Unbalanced forces sum to a nonzero net force — the object accelerates in the direction of the net force (Newton's 2nd law).

Work is done when a force causes displacement: $W = Fd\cos\theta$, where $\theta$ is the angle between the force and the direction of motion.

Power is the rate at which work is done (or energy is transferred): $P = \frac{W}{t}$, measured in watts ($1\ \text{W} = 1\ \text{J/s}$).

Mechanical advantage compares output force to input force: $MA = \frac{F_{out}}{F_{in}}$ — an $MA$ greater than 1 means the machine multiplies force.

First Peoples technologies apply the same simple-machine principles found in the formal physics of levers, wedges, and inclined planes — refined and passed down through generations of careful observation.

Ohm's law relates voltage, current, and resistance: $V = IR$.

A mechanical wave is generated by an oscillating (vibrating) source, which disturbs the medium immediately around it; the wave propagates as each particle interacts with its neighbour, passing the disturbance along — the particles themselves oscillate around a fixed position and don't travel with the wave.

Wave properties: amplitude (maximum displacement from rest), wavelength $\lambda$ (distance between repeating points), period $T$ (time for one full cycle), and frequency $f = \frac{1}{T}$ (cycles per second), linked by $v = f\lambda$.

Reflection: a wave bounces off a boundary — at a fixed end, the reflected wave inverts; at an open (free) end, it reflects without inverting.

The law of superposition: when two waves overlap, their displacements add together at each point — constructive interference (crests align, larger amplitude) or destructive interference (crest meets trough, reduced or cancelled amplitude).

Sound is a longitudinal wave — the medium's particles vibrate back and forth along the SAME direction the wave travels, creating compressions and rarefactions.

Significant figures are all the digits known reliably in a measurement, plus one estimated digit — they represent the actual precision of the measuring tool, not just how many digits you can write down.

Every measurement carries an uncertainty, usually estimated as half the smallest division on the instrument (e.g. a ruler marked in mm has an uncertainty of $\pm 0.5\ \text{mm}$) — reported as $\text{value} \pm \text{uncertainty}$.

When adding or subtracting measured values, the answer is rounded to match the LEAST precise decimal place among the values; when multiplying or dividing, the answer is rounded to match the FEWEST significant figures among the values.

Percent error compares an experimental result to a known/theoretical value: $\%\ \text{error}$$= \frac{|\text{experimental} - \text{theoretical}|}{\text{theoretical}} \times 100\%$; percent difference compares two experimental results to each other when no accepted value exists.

Leading zeros are never significant, trailing zeros after a decimal point ARE significant, and zeros between other digits are always significant — these rules let you count sig figs consistently in any measurement.