Physics Quick-Review Notes

Fundamental SI (Base) Units

• Time → $\text{s}$ (second)

• Electric current → $\text{A}$ (ampere)

• Amount of substance → $\text{mol}$ (mole)

• Temperature → $\text{K}$ (kelvin)

• Length → $\text{m}$ (meter)

• Mass → $\text{kg}$ (kilogram)

• Luminous intensity → $\text{cd}$ (candela)

• Liters ($\text{L}$) = derived (NOT a base unit)

Core Kinematics

• Average velocity: $v = \dfrac{\Delta x}{t}$

• Average speed: $s = \dfrac{\text{distance}}{t}$

• Acceleration (kinematics): $a = \dfrac{\Delta v}{t}$

Three key constant-acceleration ("family") equations

1. $v<em>f = v</em>i + a t$

2. $\Delta x = v_i t + \dfrac12 a t^2$

3. $v<em>f^2 = v</em>i^2 + 2 a \Delta x$

Uniform Circular Motion

• Centripetal (radial) acceleration: $a_c = \dfrac{v^2}{r}$

• $v$ tangent to circle; $a_c$ points to center; they are $90^{\circ}$ apart.

Units to Recall

• Velocity / speed → $\text{m\,/\,s}$

• Acceleration → \text{m\,/\,s^2}

• Force → \text{N} = \text{kg·m\,/\,s^2}

• Displacement / distance → $\text{m}$

Problem-Solving Template (GUESS)

• G – Given data

• U – Unknown quantity

• E – Equation to use

• S – Substitute

• S – Solve (include units)

Worked Examples

• Linear motion: $v<em>i = 20\,\text{m/s}$, a = 1\,\text{m/s^2}, $t = 25\,\text{s}$ ⇒ $v</em>f = 20 + (1)(25) = 45\,\text{m/s}$

• Circular motion: ac = 2\,\text{m/s^2}, $r = 8\,\text{m}$ ⇒ $v = \sqrt{a</em>c r} = \sqrt{(2)(8)} = 4\,\text{m/s}$

Significant-Figure Rules (quick)

• With decimal: start left, first non-zero → count every digit after.

• Without decimal: start right, first non-zero → count leftward; trailing zeros are NOT significant.

• Examples:
  • $7.0$ → $2$ sig figs • $0.00097$ → $2$ • $90.057$ → $5$ • $150.$ → $3$ (decimal forces zeros to count)

Interpreting Motion Graphs

• Slope of distance–time graph ⇒ velocity.

• Slope of velocity–time graph ⇒ acceleration.

• Flat $v$–$t$ line above zero → constant speed.

• Downward-sloping $v$–$t$ line → constant negative acceleration (deceleration).

• Curved $d$–$t$ graph with decreasing steepness → high acceleration initially, decreasing later.

1. Units of Measurement

1.1 Fundamental SI (Base) Units

• Time
  → $\text{s}$ (second)

• Electric current
  → $\text{A}$ (ampere)

• Amount of substance
  → $\text{mol}$ (mole)

• Temperature
  → $\text{K}$ (kelvin)

• Length
  → $\text{m}$ (meter)

• Mass
  → $\text{kg}$ (kilogram)

• Luminous intensity
  → $\text{cd}$ (candela)

• Liters ($\text{L}$) = derived (NOT a base unit)

1.2 Common Derived Units for Motion and Force

• Velocity / speed
  → $\text{m/s}$ (meters per second)

• Acceleration
  → \text{m/s^2} (meters per second squared)

• Displacement / distance
  → $\text{m}$ (meters)

• Force
  → \text{N} = \text{kg·m/s^2} (Newtons, which are kilograms times meters per second squared)

1. Kinematics and Motion Principles

2.1 Core Kinematics Formulas

• Average velocity: $v = \dfrac{\Delta x}{t}$ (change in position over time)

• Average speed: $s = \dfrac{\text{distance}}{t}$ (total distance over time)

• Acceleration (kinematics): $a = \dfrac{\Delta v}{t}$ (change in velocity over time)

2.2 Constant-Acceleration Equations ("Family" Equations)

• $\textit{v}<em>f = \textit{v}</em>i + \textit{at}$ (final velocity equals initial velocity plus acceleration times time)

• $\Delta x = \textit{v}_i \textit{t} + \frac{1}{2} \textit{a} \textit{t}^2$ (change in position equals initial velocity times time plus one-half acceleration times time squared)

• $\textit{v}<em>f^2 = \textit{v}</em>i^2 + 2\textit{a}\Delta x$ (final velocity squared equals initial velocity squared plus two times acceleration times change in position)

2.3 Uniform Circular Motion

• Centripetal (radial) acceleration: $\textit{a}_c = \dfrac{\textit{v}^2}{\textit{r}}$ (centripetal acceleration equals velocity squared divided by radius)

• $\textit{v}$ is tangent to the circle (points along the circle's edge); $\textit{a}_c$ points to the center of the circle; they are $90^{\circ}$ apart (perpendicular).

2.4 Interpreting Motion Graphs

• The slope of a distance–time graph tells you the object's velocity.

• The slope of a velocity–time graph tells you the object's acceleration.

• A flat line on a velocity–time ($\textit{v} – \textit{t}$) graph, above zero, means the object has constant speed.

• A downward-sloping line on a velocity–time ($\textit{v} – \textit{t}$) graph means the object has constant negative acceleration (it's slowing down or accelerating in the negative direction).

• A curved line on a distance–time ($\textit{d} – \textit{t}$) graph that gets less steep means the object had high acceleration initially, but it is decreasing later.

1. Problem-Solving and Data Handling

3.1 Problem-Solving Template (GUESS Method)

• G – Given data: Write down all the numerical values provided in the problem.

• U – Unknown quantity: Identify what you need to find.

• E – Equation to use: Choose the appropriate formula or equation that connects your given data to your unknown.

• S – Substitute: Plug the given numerical values into your chosen equation.

• S – Solve: Calculate the answer and make sure to include the correct units.

3.2 Worked Examples

• Linear motion: If initial velocity ($\textit{v}_i$) = $20\,\text{m/s}$, acceleration ($\textit{a}$) = 1\,\text{m/s^2}, and time ($\textit{t}$) = $25\,\text{s}$:

  Use formula: $\textit{v}<em>f = \textit{v}</em>i + \textit{at}$

  Substitute: $\textit{v}_f = 20 + (1)(25)$

  Solve: $\textit{v}_f = 45\,\text{m/s}$ (final velocity)

• Circular motion: If centripetal acceleration ($\textit{a}_c$) = 2\,\text{m/s^2} and radius ($\textit{r}$) = $8\,\text{m}$:

  Use formula: $\textit{a}<em>c = \dfrac{\textit{v}^2}{\textit{r}}$ which can be rearranged to $\textit{v} = \sqrt{\textit{a}</em>c \textit{r}}$

  Substitute: $\textit{v} = \sqrt{(2)(8)}$

  Solve: $\textit{v} = \sqrt{16} = 4\,\text{m/s}$ (speed of the object)

3.3 Significant-Figure Rules (Quick Reference – Simplified)

Significant figures (or sig figs) tell you how precise a measurement is. Here’s how to count them:

• Rule 1: If there is a decimal point in the number (Explicit Decimal)

  • Start counting from the leftmost non-zero digit.

  • Count all digits from that point, including any zeros that follow, even if they are at the very end.

  • Examples:

    • $7.0$
      → Counts 7 and 0. So, $2$ significant figures.

    • $0.00097$
      → Start at 9. Counts 9 and 7. So, $2$ significant figures.

    • $90.057$
      → Start at 9. Counts 9, 0, 0, 5, 7. So, $5$ significant figures.

    • $150.$
      → The decimal point is present. Start at 1. Counts 1, 5, 0. So, $3$ significant figures.

• Rule 2: If there is NO decimal point in the number (Implicit Decimal)

  • Start counting from the rightmost non-zero digit.

  • Count all digits leftward from that point.

  • Trailing zeros (zeros at the very end of the number) are NOT considered significant if there's no decimal point.

  • Example:

    • $150$ (no decimal point)
      → Start counting from 5 (the rightmost non-zero digit). Counts 1 and 5. The 0 is a trailing zero and is not counted. So, $2$ significant figures.