Comprehensive Physics Paper 2 Revision Guide

Scalars and Vectors

• Scalar Quantities: These are quantities that have magnitude (size) but no specific direction. Examples provided include:

  • Distance

  • Speed

  • Mass

  • Energy

  • Temperature

• Vector Quantities: These are quantities that have both magnitude and direction. Examples include:

  • Displacement

  • Velocity

  • Acceleration

  • Force

  • Momentum

Forces and Interactions

• Definition of Forces: Forces are vectors and are divided into two main categories: contact and non-contact.

• Contact Forces: Occur when objects are in physical contact.

  • Tension: Found in strings and ropes.

  • Air Resistance (Drag): Occurs when an object travels through air or a fluid.

  • Friction: A force that resists motion when two surfaces in contact move past each other.

  • Normal Contact Force: Acts between two objects that are in physical contact with each other.

• Non-Contact Forces: Occur without objects being in physical contact.

  • Electrostatic Force: Acts between charged particles.

  • Magnetic Force: Acts between magnets.

  • Gravitational Force (Weight): The force acting on an object with mass due to gravity.

• Weight: The weight of an object depends on the gravitational field strength of the planet it is on. Weight and mass are directly proportional ($W \propto m$), meaning if mass doubles, weight doubles.

  • Formula: $W = m \times g$

  • Center of Mass: Weight is considered to act at a single point on an object known as its center of mass.

Resultant Forces and Work Done

• Free Body Diagrams: Use arrows to represent forces. The size of the arrow correlates to the magnitude of the force.

• Calculating Resultant Force:

  • Same Direction: Add the forces together.

  • Opposite Direction: Subtract the smaller force from the larger force.

  • Right Angles: Use a scale drawing. Draw arrows "tip to toe," then measure the diagonal. Use the scale to convert the length back into a force value. Use a protractor to find the angle (direction).

• Resolving Forces: A diagonal force can be split into horizontal and vertical components using scale drawings. Measure the horizontal and vertical distances and use the scale to determine the magnitude of these components.

• Work Done: Work is done when a force is applied to an object, causing it to move a distance. This results in energy being transferred from one store to another.

  • Formula: $W = F \times s$

Elasticity and Deformation

• Types of Deformation: Applying two or more forces to an object can cause it to stretch, compress, or bend.

  • Elastic Deformation: The object returns to its original shape and size once forces are removed. All work done is converted into elastic potential energy.

  • Inelastic Deformation: The object does not return to its original shape. Work done is wasted as heat to the surroundings.

• Hooke’s Law: The force applied is directly proportional to the extension of an elastic object, provided the limit of proportionality is not exceeded.

  • Formula: $F = k \times e$

  • Elastic Potential Energy Formula: $E_e = \frac{1}{2} k e^2$

• Force-Extension Graphs:

  • The graph is initially a straight line through the origin, indicating Hooke’s Law is obeyed.

  • The gradient of the straight section represents the spring constant ($k$), which indicates how difficult the object is to stretch.

  • The Limit of Proportionality is the point where the graph begins to curve, and the law is no longer obeyed.

Linear Motion and Graphs

• Distance vs. Displacement:

  • Distance: A scalar quantity representing how far an object moves, regardless of direction.

  • Displacement: A vector quantity representing the overall distance and direction from the starting position to the ending position.

• Speed vs. Velocity:

  • Speed: A scalar representing how fast an object moves.

  • Velocity: A vector representing speed in a given direction.

  • Speed Formula: $v = \frac{s}{t}$

• Typical Speeds: The transcript notes that students must be aware of typical speeds for various scenarios (e.g., walking, running, cycling).

• Distance-Time Graphs:

  • Steep line: High speed.

  • Flat horizontal line: Stationary (no movement).

  • Straight sloping line: Constant speed.

  • Curved line: Acceleration or deceleration. Speed at a specific point on a curve is found by drawing a tangent and calculating its gradient.

• Velocity-Time Graphs:

  • Steepness/Gradient: Represents acceleration.

  • Flat horizontal line: Constant speed (zero acceleration).

  • Straight sloping line: Constant acceleration or deceleration.

  • Curved line: Changing acceleration.

  • Area under the graph: Represents the total distance traveled by the object.

• Acceleration Formulas:

  • $a = \frac{\Delta v}{t}$

  • $v^2 - u^2 = 2as$

Terminal Velocity, Newton’s Laws, and Momentum

• Terminal Velocity: Occurs when an object falls through a fluid (liquid or gas).

  1. Initially, weight is greater than drag, leading to acceleration.

  2. Drag (air resistance) increases as speed increases.

  3. Drag eventually becomes equal to weight.

  4. Resultant force becomes zero; the object reaches a constant maximum speed called terminal velocity.

• Newton’s First Law: If forces are balanced (resultant force is zero), an object remains stationary or continues at a constant speed.

• Newton’s Second Law: If forces are unbalanced, the object will accelerate. Force and acceleration are directly proportional.

  • Formula: $F = m \times a$

• Newton’s Third Law: When two objects interact, they exert equal and opposite forces on each other. (e.g., pushing a wall with $50\,N$ results in the wall pushing back with $50\,N$ in the opposite direction).

• Inertia: The tendency of an object to resist changes in its state of motion.

  • Inertial Mass: A measure of how difficult it is to change velocity. It is the ratio of force over acceleration ($m = \frac{F}{a}$). A bowling ball has higher inertial mass than a basketball.

• Stopping Distance: The total distance required for a vehicle to stop from the moment a hazard is spotted.

  • Stopping Distance = Thinking Distance + Braking Distance.

  • Thinking Distance: Distance traveled during reaction time. Affected by alcohol, drugs, tiredness, and distractions.

  • Braking Distance: Distance traveled after brakes are applied. Affected by road conditions, tire/brake conditions, and weather.

  • Speed: Affects both thinking and braking distances.

  • Physics of Braking: Work is done by friction between the brakes and wheels, converting kinetic energy into thermal energy. This increases the temperature of the brakes.

• Momentum: A property of all moving objects.

  • Formula: $p = m \times v$

  • Conservation of Momentum: In a closed system, the total momentum before a collision is equal to the total momentum after the collision.

Waves

• General Properties: Waves transfer energy without transferring matter by causing particles to oscillate (vibrate).

• Types of Waves:

  • Transverse Waves: Oscillations are perpendicular to the direction of energy transfer (e.g., water waves, electromagnetic waves). Features include peaks (top) and troughs (bottom).

  • Longitudinal Waves: Oscillations are parallel to the direction of energy transfer (e.g., sound waves). Features include compressions (particles close together) and rarefactions (particles far apart).

• Wave Measurements:

  • Amplitude: Maximum displacement from the rest position (center).

  • Wavelength (\lambda): Distance between two adjacent peaks/troughs (transverse) or adjacent compressions (longitudinal).

  • Frequency (f): Number of waves passing a point per second. Measured in hertz ($Hz$).

  • Period (T): Time taken for one complete wave to pass.

• Wave Equations:

  • $T = \frac{1}{f}$

  • $v = f \times \lambda$

• Wave Interactions at Boundaries:

  • Reflection: Bouncing off a material.

  • Absorption: Energy transferred to the material.

  • Transmission: Passing through the material.

  • Refraction: A change in direction caused by a change in speed when entering a new medium. Moving from less dense to more dense material bends the wave toward the normal. Moving from high to low density bends it away from the normal.

The Electromagnetic (EM) Spectrum

• Properties: Transverse waves that travel at the same speed in a vacuum ($3 \times 10^8\,m/s$).

• Spectrum Order (Decreasing Wavelength / Increasing Frequency):

  1. Radio Waves: Used for wireless communication. Generated by alternating current in a transmitter (oscillating electrons). The receiver absorbs them, recreating the current.

  2. Microwaves: Used for satellite communication (penetrate atmosphere) and cooking (vibrate water molecules).

  3. Infrared (IR): Used in heaters and IR cameras (hotter objects appear brighter).

  4. Visible Light: Used in fiber optic communication (minimal signal loss over long distances). Colors: Red, Orange, Yellow, Green, Blue, Indigo, Violet.

  5. Ultraviolet (UV): Used in tanning beds and energy-efficient lamps (converted back to visible light).

  6. X-rays: Used for medical imaging.

  7. Gamma Rays: Used for medical imaging and cancer treatment.

• Hazards and Atomic Changes:

  • EM waves can move electrons to higher energy levels (when absorbed) or lower levels (when emitted).

  • UV: Causes premature skin aging and increased skin cancer risk.

  • X-rays and Gamma Rays: Ionizing radiation that causes DNA damage and cancer risk. Impact depends on the type of radiation and the dose, measured in Sieverts.

Magnetism and Electromagnetism

• Magnetic Poles: Opposite poles attract; like poles repulse.

• Magnetic Materials: Iron, steel, nickel, and cobalt.

• Magnetic Fields: A region where a magnet or current-carrying wire experiences a force.

  • Field Lines: Point from North to South. Closer lines indicate a stronger field (strongest at the poles).

  • Plotting Fields: Can be done using a compass and plotting points as it moves.

• Permanent vs. Induced Magnets:

  • Permanent: Produces its own field.

  • Induced: A magnetic material that becomes a magnet only when placed in a magnetic field. It always creates an attractive force.

• Electromagnetism:

  • Current in a wire creates a magnetic field made of concentric circles.

  • Right-Hand Grip Rule: Thumb points in direction of current; fingers show the direction of the magnetic field.

  • Solenoid: Coiled wire that creates a strong, uniform magnetic field inside (like a bar magnet outside).

  • Electromagnet: A solenoid with an iron core that can be turned on and off.

The Motor Effect

• Definition: A current-carrying wire in an external magnetic field experiences a force.

• Force Equation: $F = B \times I \times L$

• Fleming’s Left-Hand Rule:

  • First Finger: Magnetic Field (North to South).

  • Second Finger: Current.

  • Thumb: Direction of Force (Motion).

• Electric Motors: Utilize a coil of wire in a magnetic field. Opposite forces on each side of the coil cause rotation. A split ring commutator reverses the current every half turn to keep the motor spinning in the same direction.

Questions & Discussion

• Question: Which of the following is a scalar quantity?

  • Answer: Temperature.

• Question: Which of the following is a vector quantity?

  • Answer: Force.

• Question: Which of these forces is an example of a non-contact force?

  • Answer: Gravitational force.

• Question: In which type of waves do oscillations travel parallel to the direction of energy transfer?

  • Answer: Longitudinal waves.

• Question: What is the definition for the amplitude of a wave?

  • Answer: It is the maximum displacement of a point on a wave from its rest position.

• Question: What unit is frequency measured in?

  • Answer: It's measured in hertz ($Hz$).

• Question: Which of the following is a transverse wave?

  • Answer: Visible light (part of the EM spectrum).

• Question: In which direction do magnetic field lines point outside a bar magnet?

  • Answer: They always point from north to south.

• Question: When using the right-hand grip rule for a current-carrying wire, what direction does the thumb point in?

  • Answer: It points in the direction of the current.