Physics NOV

The 7 base SI units and their corresponding base quantities

• Mass: kilogram ($\text{kg}$)
• Length: metre ($\text{m}$)
• Time: second ($\text{s}$)
• Electric current: ampere ($\text{A}$)
• Temperature: kelvin ($\text{K}$)
• Amount of substance: mole ($\text{mol}$)
• Luminous intensity: candela ($\text{cd}$)

Derived units and dimensional consistency in physics

• Derived unit: A unit created by multiplying or dividing base units (e.g., $1\,\text{N} = 1\,\text{kg}\,\text{m}\,\text{s}^{-2}$).
• Dimensional consistency: An equation is dimensionally consistent if both sides reduce to the exact same combination of base SI units.

Metric unit prefixes from pico to tera

• pico ($\text{p}$): $10^{-12}$
• nano ($\text{n}$): $10^{-9}$
• micro ($\mu$): $10^{-6}$
• milli ($\text{m}$): $10^{-3}$
• kilo ($\text{k}$): $10^3$
• mega ($\text{M}$): $10^6$
• giga ($\text{G}$): $10^9$
• tera ($\text{T}$): $10^{12}$

Differences between scalar and vector quantities

• Scalar: Has magnitude only. Examples include mass, distance, speed, and energy.
• Vector: Has both magnitude and direction. Examples include displacement, velocity, acceleration, force, and momentum.

Techniques for adding, subtracting, and resolving vectors

• Addition and subtraction: Combine using tip-to-tail vector diagrams or using trigonometry and the Pythagorean theorem.
• Vector resolution: For a vector $V$ at an angle $\theta$ to the horizontal:
  • Horizontal component: $V_x = V \cos(\theta)$
  • Vertical component: $V_y = V \sin(\theta)$

Key kinematic definitions: displacement, speed, velocity, and acceleration

• Displacement ($s$): Straight-line distance in a specified direction ($\text{m}$).
• Speed: Rate of change of distance ($\text{m}\,\text{s}^{-1}$).
• Velocity ($v$): Rate of change of displacement ($\text{m}\,\text{s}^{-1}$).
• Acceleration ($a$): Rate of change of velocity ($\text{m}\,\text{s}^{-2}$).

Interpretation of gradients and areas on motion graphs

• Displacement-time graph: Gradient = velocity.
• Velocity-time graph: Gradient = acceleration; area under graph = displacement ($s$).
• Acceleration-time graph: Area under graph = change in velocity ($\Delta v$).

The 4 SUVAT equations for uniform acceleration

• $v = u + at$
• $s = \frac{1}{2}(u + v)t$
• $s = ut + \frac{1}{2}at^2$
• $v^2 = u^2 + 2as$

Principles and modeling of projectile motion under gravity

• Perpendicular motions are completely independent.
• Horizontal motion: Constant velocity with zero acceleration ($a_x = 0$), governed by $s_x = v_x t$.
• Vertical motion: Uniform acceleration downwards due to gravity ($a_y = -g = -9.81\,\text{m}\,\text{s}^{-2}$).

Laboratory measurement of velocity and acceleration using light gates

• Velocity: A card of known length $d$ interrupts a light gate for time $t$, giving instantaneous velocity $v = \frac{d}{t}$.
• Acceleration: A double interrupt card or two spaced light gates record initial velocity $u$, final velocity $v$, and time interval $t$ to calculate acceleration using $a = \frac{v - u}{t}$ or $v^2 = u^2 + 2as$.

Newton's Three Laws of Motion

• First Law: An object remains at rest or at constant velocity unless acted upon by a net external force.
• Second Law: The net force is proportional to the rate of change of momentum: $F = \frac{\Delta p}{\Delta t} = ma$.
• Third Law: If body A exerts a force on body B, body B exerts an equal and opposite force of the same type on body A.

Distinctions between mass, weight, and center of gravity

• Mass ($m$): The amount of matter in an object ($\text{kg}$, scalar, invariant).
• Weight ($W$): Gravitational pull on a body ($W = mg$, $\text{N}$, vector, varies with $g$).
• Center of Gravity: The single point through which the entire weight of an object is considered to act.

Free-body diagrams and the properties of friction

• Free-body diagram: A vector diagram showing all external forces acting exclusively on a single isolated object.
• Friction: A contact force that always acts parallel to the interface and opposes the relative motion or intended motion between surfaces.

Definitions and relationships of linear momentum and impulse

• Linear Momentum ($p$): The product of mass and velocity: $p = mv$ ($\text{kg}\,\text{m}\,\text{s}^{-1}$ or $\text{N}\,\text{s}$).
• Impulse: Change in momentum given by $\Delta p = F \Delta t = mv - mu$, which equals the area under a force-time graph.

Principle of Conservation of Linear Momentum in 1D and 2D

• For a closed system with no external resultant forces, total linear momentum is conserved before and after an interaction.
• In two dimensions, momentum is conserved independently in perpendicular directions:
  • $\sum p_{x,\text{initial}} = \sum p_{x,\text{final}}$
  • $\sum p_{y,\text{initial}} = \sum p_{y,\text{final}}$

Differences between elastic and inelastic collisions

• Elastic collision: Both total momentum and total kinetic energy are conserved.
• Inelastic collision: Momentum is conserved, but kinetic energy is not conserved (energy is transformed into thermal energy, sound, or deformation).

Methods for calculating work done by constant and variable forces

• Constant force at an angle $\theta$ to motion: $W = F x \cos(\theta)$
• Variable force: Work done equals the area under a force-displacement ($F$-$x$) graph.

The Principle of Conservation of Energy

• Energy cannot be created or destroyed, only transferred from one store to another.
• The total energy of an isolated system remains constant over time.

Kinetic and potential energy formulas and the derivation of kinetic energy

• Formulas: $E_k = \frac{1}{2}mv^2$ and $\Delta E_p = mgh$
• Derivation:
  • Work done is $W = Fs$.
  • By Newton's second law, $F = ma$, giving $W = mas$.
  • From kinematics with $u = 0$, $v^2 = 2as \implies as = \frac{1}{2}v^2$.
  • Substituting yields $W = m\left(\frac{1}{2}v^2\right) = \frac{1}{2}mv^2$.

Definition and fundamental formulas for power

• Definition: Power is the rate of energy transfer or work done ($1\,\text{W} = 1\,\text{J}\,\text{s}^{-1}$).
• General: $P = \frac{W}{t} = \frac{\Delta E}{t}$
• Electrical: $P = IV$
• Mechanical: $P = Fv$ (for a force acting at constant speed $v$)

Definition and formula for efficiency

• $\text{Efficiency } \eta = \frac{\text{Useful Energy (or Power) Output}}{\text{Total Energy (or Power) Input}} \times 100\%$

Tensile vs. compressive forces, Hooke's Law, and force-extension graphs

• Tensile forces stretch an object, whereas compressive forces squish or shorten it.
• Hooke's Law: Extension $x$ is directly proportional to applied force $F$ up to the limit of proportionality: $F = kx$.
• Force-extension graph: Displays a straight line through the origin up to the limit of proportionality, where gradient equals stiffness $k$.

Key mechanical limits and transition points on a stress-strain curve

• Elastic limit: The maximum stress beyond which a material deforms plastically and will not return to its original length.
• Yield point: The point at which a small stress increase causes a large, permanent plastic strain.
• Ultimate Tensile Strength (UTS): The maximum stress a material can withstand before necking begins.
• Breaking point: The stress at which the material fractures.

Stress, strain, and Young modulus definitions and experimental measurement

• Tensile stress: $\sigma = \frac{F}{A}$ ($\text{Pa}$ or $\text{N}\,\text{m}^{-2}$)
• Tensile strain: $\varepsilon = \frac{\Delta l}{l_0}$ (dimensionless)
• Young modulus: $E = \frac{\sigma}{\varepsilon} = \frac{F l_0}{A \Delta l}$ (gradient of linear region of stress-strain graph)
• Measurement: Hang loads $F = mg$ on a long wire of original length $l_0$ measured with a tape measure; record diameter $d$ with a micrometer ($A = \frac{\pi d^2}{4}$); determine extension $\Delta l$ using a vernier scale; plot $\sigma$ against $\varepsilon$.

Elastic strain energy calculation from a force-extension graph

• Elastic strain energy equals the area under the force-extension curve:
• $\text{Strain Energy} = \frac{1}{2} F x = \frac{1}{2} k x^2$

Distinction between elastic and plastic deformation

• Elastic deformation: The material returns to its original dimensions when the deforming load is removed; stored strain energy is fully recoverable.
• Plastic deformation: The material experiences permanent set and does not return to its original shape; work done is dissipated primarily as thermal energy.