OCR AS Level Physics Comprehensive Study Notes

Vectors and Scalars

• Forces are represented using vectors, which are arrows indicating both the magnitude (strength) and the direction of the force.

• If two forces act on an object, the overall effect is the resultant force, found by adding the vectors.

• When forces act in opposite directions, one must be designated as negative. For example, if positive is to the right, a force of $8\,N$ right and $5\,N$ left results in a resultant force of $3\,N$ to the right.

• If forces act at right angles to each other, the resultant is found using Pythagoras’ theorem. This is possible by "top and tailing" the vectors to form a right-angled triangle.

• Trigonometry ($\sin(\theta)$, $\cos(\theta)$, $\tan(\theta)$, abbreviated as "SOH CAH TOA") is used to calculate specific angles within these vector triangles.

• A scalar quantity has magnitude only, with no direction.

• Examples include:

  • Scalars: Distance, Speed, Mass, Energy, Temperature.

  • Vectors: Displacement (distance in a direction), Velocity (speed in a direction), Acceleration, Force, Weight (force due to gravity).

Weight, Work Done, and Power

• Weight is the force acting on a mass due to a gravitational field.

• It is calculated using the formula: $W = m \times g$.

  • $m$ is mass in $\text{kg}$.

  • $g$ is gravitational field strength, which is $9.8\,N\,kg^{-1}$ (or $9.8\,m/s^2$) on Earth.

• To hold an object stationary, an upward force equal to its weight must be applied so forces are balanced ($a = 0$). This also applies when lifting an object at a constant speed.

• Work Done ($W$) is equivalent to the energy transferred by a force. The formula is: $W = F \times s$.

  • $F$ is force in Newtons.

  • $s$ is distance moved in meters.

• When lifting an object, the force is the weight and the distance is the height ($h$). Therefore, work done equals the gain in Gravitational Potential Energy (GPE): $GPE = m \times g \times h$.

• For the work done equation to be valid, the force and distance moved must be parallel. If they are at an angle $\theta$, we resolve the force using the formula: $W = F \times s \times \cos(\theta)$.

• Power ($P$), often called power developed, is the rate of work done (work divided by time). It can be calculated as: $P = F \times v$.

  • $v$ is the velocity of the object.

Newton’s Laws of Motion and Inclined Planes

• Newton’s First Law: When there is no resultant force acting on an object, its motion is constant (zero change in velocity). This occurs when all forces are balanced or no forces act at all.

• Newton’s Second Law: When forces are unbalanced, the resultant force ($F$) is equal to mass ($m$) multiplied by acceleration ($a$): $F = m \times a$.

• Newton’s Third Law: For every action (force), there is an equal and opposite reaction force. This is not referring to balanced forces on a single object, but forces between two bodies.

  • Example: Earth pulls down on a ball (weight); the ball pulls the Earth up with an equal force.

  • Example: Two ice skaters pushing each other move away in opposite directions due to reaction forces.

• Objects on slopes:

  • The weight ($m \times g$) acts vertically downwards.

  • The reaction force from the slope acts perpendicular to the surface and is equal to $m \times g \times \cos(\theta)$.

  • The component of weight pulling the object down the slope (parallel to the surface) is $m \times g \times \sin(\theta)$.

  • If the object is stationary or at a constant speed, an opposing force (like friction) must equal $m \times g \times \sin(\theta)$.

• Energy on a ramp: If no friction exists, energy converts perfectly: $m \times g \times h = \frac{1}{2} \times m \times v^2$. If energy is lost, the work done against friction is used to find average frictional force over the distance traveled.

Projectile Motion and SUVAT

• Equations of motion (SUVAT) are used for constant acceleration:

  • $s$: displacement

  • $u$: initial velocity

  • $v$: final velocity

  • $a$: acceleration

  • $t$: time

• Vertical and horizontal motion are treated separately.

• For objects thrown vertically and returning to Earth: It is best to split the problem in half ($v=0$ at the apex) and double the time.

• Objects fired horizontally (e.g., off a cliff):

  • Vertical motion: $u = 0$, $a = g = 9.81\,m/s^2$, and $s = \text{height}$. Usually, $s = \frac{1}{2} \times a \times t^2$ because $u=0$.

  • Horizontal motion: Velocity remains constant. Use $\text{speed} = \frac{\text{distance}}{\text{time}}$.

• Objects fired at an angle: Resolve the initial velocity into horizontal and vertical components using trigonometry before applying the methods above.

Momentum and Collisions

• Momentum ($p$) is the product of mass and velocity: $p = m \times v$. The unit is $kg\,m/s$.

• Momentum is a vector; direction must be accounted for with positive and negative values.

• Conservation of Momentum: Total momentum before a collision equals total momentum after.

  • Total Initial Momentum: $m_1 \times u_1 + m_2 \times u_2$.

  • Total Final Momentum: $m_1 \times v_1 + m_2 \times v_2$.

• Rebound and Recoil:

  • Rebound off a wall: Change in momentum (impulse) is calculated as $-2mv$ (if hitting a wall at $u$ and rebounding at $-u$).

  • Recoil (e.g., a cannon): Total initial momentum is $0$. After firing, the cannonball and cannon have equal but opposite momentum.

• Elastic vs. Inelastic:

  • Elastic collision: Total kinetic energy ($E_k$) is conserved (e.g., snooker balls).

  • Inelastic collision: Kinetic energy is lost as heat, sound, or deformation (e.g., plasticine balls colliding).

• Impulse and Force:

  • Force is the rate of change of momentum: $F = \frac{\Delta (mv)}{t}$. The unit of momentum can also be written in Newton-seconds ($N\,s$).

  • On a force-time graph, the area under the curve is the impulse ($\Delta p$).

• Fluid Forces: Force from a fluid (like air or water) can be derived as $F = \rho \times A \times v^2$, where $\rho$ is density and $A$ is cross-sectional area.

Moments, Torque, and Equilibrium

• A moment (or torque) is a turning force around a pivot.

• Formula: $\text{Moment} = \text{Force} \times \text{perpendicular distance from the pivot}$. Unit: $N\,m$.

• If force is not perpendicular, use trigonometry ($F \times d \times \cos(\theta)$ or $F \times d \times \sin(\theta)$) to find the perpendicular component.

• Principle of Moments: For an object in equilibrium, the sum of clockwise moments must equal the sum of anticlockwise moments ($\sum M_{CW} = \sum M_{ACW}$).

• Conditions for Equilibrium:

  1. No resultant force ($\sum F = 0$).

  2. No resultant moment ($\sum M = 0$).

• Couples: Two equal forces acting in opposite directions, separated by a distance, resulting in a moment (rotation) but no net translation (no resultant force).

• Toppling: An object topples when its center of gravity moves past the pivot vertically, reversing the direction of the weight's moment.

Materials and Deformation

• Hooke’s Law: $F = k \times \Delta L$ (or $F = kx$), where $k$ is the spring constant/stiffness and $\Delta L$ is extension.

  • Elastic deformation: Material returns to original shape when the force is removed.

  • Energy stored (Elastic Potential Energy) is the area under the force-extension graph.

• Spring Combinations:

  • In Series: Extension doubles, so equivalent $k_{eff} = \frac{1}{2}k$.

  • In Parallel: Extension halves, so equivalent $k_{eff} = 2k$.

• Young Modulus ($E$): A measure of material stiffness.

  • Stress ($\sigma$): Force per unit area ($\sigma = \frac{F}{A}$), measured in Pascals ($Pa$).

  • Strain ($\epsilon$): Ratio of extension to original length ($\epsilon = \frac{\Delta L}{L}$), dimensionless.

  • Formula: $E = \frac{\sigma}{\epsilon} = \frac{F \times L}{A \times \Delta L}$.

• Behavior of Materials:

  • Limit of Proportionality: Past this, stress and strain are no longer directly proportional.

  • Elastic Limit: Past this, deformation becomes plastic (permanent).

  • Ultimate Tensile Strength (UTS): The maximum stress a material can withstand.

  • Ductile materials (copper) exhibit large plastic regions. Brittle materials have high Young modulus but snap suddenly.

Electricity Basics: Current, Voltage, and Resistance

• Current ($I$): The rate of flow of charge ($Q$). Formula: $I = \frac{Q}{t}$. Unit: Amperes ($A$).

• Conventional current flows from the positive terminal to the negative terminal.

• Potential Difference ($V$): Energy ($E$) transferred per unit charge. Formula: $V = \frac{E}{Q}$. Unit: Volts ($V$). A $6\,V$ battery supplies $6\,J$ per Coulomb.

• Resistance ($R$): Opposes the flow of charge. Ohm's Law: $V = I \times R$.

• Components:

  • Ohmic Resistors: Constant resistance; graph is a straight line through the origin.

  • Filament Lamp: Non-ohmic; resistance increases with current as metal ions vibrate more due to heating.

  • Diodes: Allow current flow in one direction only (forward bias starting at approximately $1.0\,V$).

• Superconductors: Materials with zero resistance below a specific critical temperature ($T_c$).

• Resistivity ($\rho$): Characteristic property of a material. Formula: $\rho = \frac{R \times A}{L}$. Unit: $\Omega\,m$.

DC and AC Circuits

• Series Circuits:

  • Current is the same everywhere.

  • Total potential difference ($V_{total}$) is shared between components.

  • Total Resistance ($R_{total}$) is the sum of all individual resistances.

• Parallel Circuits:

  • Potential difference ($V$) is the same across every branch.

  • Total current ($I_{total}$) is shared between branches (Kirchhoff’s First Law).

  • Adding resistors in parallel decreases total resistance because it provides more paths for charge.

• Kirchhoff’s Second Law: Sum of EMFs equals the sum of PD drops in any closed loop ($\sum \epsilon = \sum IR$).

• Sensors:

  • Negative Temperature Coefficient (NTC) Thermistor: Resistance decreases as temperature increases.

  • Light Dependent Resistor (LDR): Resistance decreases as light intensity increases.

• Mains Electricity (AC):

  • Live wire varies between $+325\,V$ and $-325\,V$ (Peak voltage).

  • Root Mean Square (RMS) voltage in the UK is $230\,V$. Calculation: $V_{RMS} = \frac{V_{peak}}{\sqrt{2}}$.

• Internal Resistance ($r$):

  • EMF ($\epsilon$) is the total potential difference provided.

  • Terminal PD ($V$) is the voltage across the external circuit.

  • Formula: $\epsilon = V + I \times r$.

  • Graphing $V$ vs. $I$: Y-intercept is EMF, gradient magnitude is $r$.

Waves and Light

• Longitudinal waves: Oscillations are parallel to energy transfer (e.g., sound).

• Transverse waves: Oscillations are perpendicular to energy transfer (e.g., light).

• Wave Properties:

  • Amplitude ($A$): Maximum displacement from equilibrium.

  • Wavelength ($\lambda$): Length of one complete cycle.

  • Frequency ($f$): Waves per second ($f = \frac{1}{T}$, where $T$ is time period).

  • Wave equation: $v = f \times \lambda$ (or $c = f \times \lambda$ for light).

  • Intensity ($I$) is proportional to Amplitude squared ($I \propto A^2$).

• Refraction and Reflection:

  • Refractive Index ($n$): Ratio of speed of light in vacuum to speed in medium ($n = \frac{c}{v}$).

  • Snell’s Law: $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$.

  • Total Internal Reflection (TIR): Occurs when the angle of incidence exceeds the critical angle ($\theta_c$).

  • Critical Angle formula: $\sin(\theta_c) = \frac{n_2}{n_1}$.

• Fiber Optics:

  • Uses TIR to transmit data. Layers include core, cladding (low refractive index), and protective sheath.

  • Problems: Modal dispersion (different paths take different times) causing pulse broadening.

• Polarization: Restricting wave oscillations to a single plane. Polarizing filters reduce light intensity by half.

Superposition and Quantum Physics

• Phase Difference: Measured in degrees ($360^\circ$ per cycle) or radians ($2\pi$\,rad per cycle).

• Stationary Waves: Formed by the superposition of two waves traveling in opposite directions. Points with zero displacement are nodes; maximum displacement are antinodes.

  • First Harmonic (String): $L = \frac{\lambda}{2}$. Frequency: $f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$, where $T$ is tension and $\mu$ is mass per unit length.

• Interference:

  • Young’s Double Slit: $w = \frac{\lambda \times D}{s}$.

  • Bright fringes (maxima): Path difference is $n\lambda$.

  • Dark fringes (minima): Path difference is $(n + 0.5)\lambda$.

• Quantum Levels:

  • Electrons exist in discrete energy levels ($n = 1, 2, 3$).

  • Excitation: Absorbing a photon or colliding with an electron to move to a higher level.

  • De-excitation: Moving to a lower level, emitting a photon with energy $E = h \times f$.

• Photoelectric Effect: Evidence for light as a particle.

  • Photons act in 1-to-1 interactions.

  • Equation: $hf = \Phi + E_{k,max}$, where $\Phi$ is the Work Function.

  • Threshold frequency ($f_0$): $\Phi = h \times f_0$.

• De Broglie Wavelength: Particles act as waves: $\lambda = \frac{h}{p} = \frac{h}{mv}$.

Practical Skills and Uncertainties

• Errors:

  • Random errors (e.g., parallax, reaction time) are inconsistent; reduced by repeats and means.

  • Systematic errors (e.g., zero error) are constant; fixed by calibration.

• Resolution:

  • Ruler: $1\,mm$.

  • Micrometer: $0.01\,mm$.

  • Vernier Caliper: $0.1\,mm$ or $0.05\,mm$.

• Significant Uncertainties:

  • Absolute uncertainty: Range / 2, or equal to resolution for single measurements.

  • Percentage uncertainty: $\frac{\text{Absolute Uncertainty}}{\text{Value}} \times 100$.

• Combining Uncertainties:

  • Adding/Subtracting: Add absolute uncertainties.

  • Multiplying/Dividing: Add percentage uncertainties.

• Log Graphs:

  • If $y = x^n$, then $\log(y) = n \times \log(x) + \text{constant}$. The gradient is the power $n$.

  • Base-10 or Natural Log ($ln$) can be used.