IMAT Physics Formula Compendium

This section lays the foundation for all physics topics by defining fundamental concepts related to measurement, units, and vector operations. A deep understanding of this area is essential, as problems involving unit conversions and formula manipulations are frequently encountered.

1.1 Basic and Derived Physical Quantities

Physics is built on accurately defined quantities, categorized into independent basic physical quantities (or base quantities) and derived physical quantities, which are expressed from basic quantities. In the International System of Units (SI), the following seven basic quantities form the foundation of measurement:

• Length: meter (m)
• Mass: kilogram (kg)
• Time: second (s)
• Electric Current: ampere (A)
• Thermodynamic Temperature: kelvin (K)
• Amount of Substance: mole (mol)
• Luminous Intensity: candela (cd)

From these basic units, many derived quantities are derived. For example, velocity is in meters per second (m/s), acceleration in meters per second squared (m/s²), force in newtons (N = kg·m/s²), pressure in pascals (Pa = N/m²), energy in joules (J = N·m), power in watts (W = J/s), charge in coulombs (C = s·A), and electrical resistance in ohms (Ω = V/A). Physical concepts are not isolated but form a coherent, interconnected framework. Understanding how derived units are expressed as combinations of basic units helps not just in memorizing units but in intuitively grasping their relationships. This understanding provides a deeper insight into the structure of physics and a powerful tool for self-checking the accuracy of formulas.

1.2 Systems of Units (SI)

The International System of Units (SI) is the globally recognized standard for scientific and technical measurement, ensuring consistency and comparability across different fields and regions. IMAT exam questions predominantly use SI units, making familiarity with them essential. SI prefixes are standardized multipliers used to express very large or small values concisely and clearly. For example, 1 kilometer (km) is equal to 10³ meters (m), and 1 microsecond (µs) is equal to 10⁻⁶ seconds (s). Prefixes range widely, from quetta (10³⁰) to quecto (10⁻³⁰). Scientific notation is the standard method for writing very large or small numbers that are inconvenient to write in decimal form. It is crucial for handling calculations involving such numbers. The format is a × 10ⁿ, where 'a' is typically a floating-point number between 1 and 10 (or 0 and 10), and 'n' is an integer exponent of 10.

1.3 Vector Operations

Vectors are physical quantities that have both magnitude and direction. In contrast, scalars are quantities with only magnitude. Examples of vectors in physics include displacement, velocity, acceleration, and force.

Vector Addition

There are two main graphical methods for adding vectors:

• Draw the first vector as an arrow.
• Place the tail of the second vector at the head of the first vector. If there are more than two vectors, repeat this process for each vector.
• Draw an arrow from the tail of the first vector to the head of the last vector. This is the resultant vector (or sum).
• Measure the magnitude of the resultant vector and its angle relative to a reference frame to determine its direction.

📸 Source/Description: Figure 1: This figure shows vector A and vector B being added head-to-tail. The resultant vector R extends from the starting point of the first vector to the endpoint of the last vector.

• Draw the two vectors to be added (e.g., P and Q) with their tails touching.
• Complete the parallelogram using these vectors as adjacent sides.
• The diagonal of the parallelogram drawn from the common tail represents the sum (resultant vector R) of the two vectors.
• Measure the magnitude of the resultant vector and its angle relative to a reference frame to determine its direction.

The magnitude of the resultant vector can be calculated using the formula:

Where P and Q are the magnitudes of the vectors, and is the angle between them. The direction of the resultant vector R (angle with respect to vector P) can be found using:

📸 Source/Description: Figure 2: This figure illustrates the Parallelogram method for vector addition. Both methods yield the same resultant vector R.

Special Cases:

• Parallel (Same Direction): When , the magnitude of the resultant vector is simply the sum of the magnitudes of the individual vectors: R = P + Q.
• Opposite Direction: When , the magnitude of the resultant vector is the absolute difference of the magnitudes of the individual vectors: R = |P - Q|.
• Perpendicular: When , the magnitude of the resultant vector is found using the Pythagorean theorem: .

Vector Subtraction

Subtracting vector B from vector A is the same as adding the negative of vector B (-B) to vector A. A negative vector is defined as a vector with the same magnitude as the original vector but in the opposite direction. Therefore, .

Multiplication of a Vector by a Scalar

Multiplying a vector by a scalar quantity c results in a new vector whose magnitude is the absolute value of c times the original magnitude. If the scalar c is positive, the direction of the vector remains unchanged. If the scalar c is negative, the direction of the vector is reversed.

Unit Conversion and Formula Manipulation

IMAT exams frequently feature problems requiring unit conversion and formula manipulation. This indicates the importance of not just memorizing formulas, but also understanding the relationships between physical quantities and the principles of dimensional analysis. Unit conversions are systematically handled by multiplying by a conversion factor equal to one, such that the desired unit replaces the original unit.

Common Unit Conversion Examples:

• To convert km/h to m/s, multiply by or the simplified fraction . Example: .
• 1 m = 100 cm
• 1 kg = 1000 g

This skill is essential for accurately solving physics problems. By carefully tracking units, you can ensure the accuracy of your calculations and maintain physical meaning.

Kinematics is the branch of physics that describes the motion of objects without considering the forces that cause the motion.

2.1 Parameters of Motion

Several basic parameters are used to describe the motion of an object:

• Displacement (s or x): The change in an object's position. It is a vector quantity.
• Velocity (v): The rate of change of displacement with respect to time. It is a vector quantity.
• Acceleration (a): The rate of change of velocity with respect to time. It is a vector quantity.
• Time (t): The duration over which motion occurs.

2.2 Uniform Rectilinear Motion

Uniform rectilinear motion is the motion of an object along a straight line at a constant velocity, which means the acceleration is zero.

Where is velocity, is displacement, and is the time interval. Example: A train traveling on a straight track at a constant speed.

2.3 Uniformly Accelerated Motion

Uniformly accelerated motion is the motion of an object with a constant acceleration. This means the object's velocity changes linearly with time. The key kinematic equations (SUVAT equations) are:

• Final Velocity:
• Displacement:
• Displacement (using average velocity):
• Final Velocity Squared:
• Displacement (using final velocity):

Where is initial velocity, is final velocity, is acceleration, is time, and is displacement. Examples include an object in free fall under gravity or a ball rolling down a frictionless ramp. It is crucial to follow a sign convention for direction when using these formulas.

2.4 Advanced Kinematics: Non-Uniform Acceleration

While IMAT focuses on constant acceleration, top-tier understanding involves cases where acceleration changes. This requires calculus. If acceleration is a function of time, velocity and position are found by integration:

A common example is an object falling with air resistance, where acceleration decreases as velocity increases, approaching a terminal velocity. While you won't likely need to perform complex integrations, understanding this conceptual link is a hallmark of advanced knowledge.

2.5 Uniform Circular Motion

Uniform circular motion is the motion of an object in a circular path at a constant speed. While the speed is constant, the direction of the velocity is always changing, so the object is always accelerating. This acceleration is called centripetal acceleration and is always directed towards the center of the circle.

• Angular Velocity: , where T is the period.
• Tangential Velocity: , where r is the radius of the circle.
• Centripetal Acceleration: . This acceleration always points towards the center of the circle.
• Centripetal Force: . The net force, like the centripetal acceleration, always points towards the center of the circle.

Example: A racing car traveling at a constant tangential speed on a circular track.

📸 Source/Description: Figure 3: This diagram shows an object moving in a circular path, with a tangential velocity vector and a centripetal acceleration vector directed toward the center. The two vectors are always perpendicular.

2.6 Simple Harmonic Motion (SHM)

Simple Harmonic Motion is a type of periodic motion where the restoring force is directed towards the equilibrium position and is directly proportional to the displacement from that position.

Key Characteristics:

• Oscillatory Motion: The object moves back and forth over the same path.
• Restoring Force: The motion is always driven by a force directed towards an equilibrium position.
• Hooke's Law: Often described using the spring force: .
• Constant Period and Frequency: The time for each complete cycle of motion is constant.

Formulas:

• Displacement: or , where A is amplitude, ω is angular frequency, and φ is the phase constant.
• Velocity: (or ).
• Acceleration: . Acceleration is always opposite to displacement.
• Angular Frequency (mass-spring system): , where k is the spring constant and m is mass.
• Period:
• Frequency: .

Examples: a mass attached to a spring on a frictionless surface, a pendulum clock, the vibration of a tuning fork.

2.7 Motion Graphs (Position, Velocity, Acceleration vs. Time)

The motion of an object can be visually represented by graphs of position, velocity, and acceleration versus time. Understanding the relationship between these graphs is essential for analyzing motion.

Position-Time Graph:

• The value on the Y-axis represents position.
• The slope represents velocity.
• A constant positive slope indicates constant positive velocity (uniform motion).
• A changing slope (a curve) indicates changing velocity (accelerated motion).
• A horizontal line means the object is at rest (zero velocity).

Velocity-Time Graph:

• The value on the Y-axis represents velocity.
• The slope represents acceleration.
• A horizontal line indicates constant velocity (zero acceleration).
• A positive slope indicates positive acceleration (speeding up).
• A negative slope indicates negative acceleration (slowing down).
• The area under the curve represents displacement.

Acceleration-Time Graph:

• The value on the Y-axis represents acceleration.
• A horizontal line indicates constant acceleration.
• The area under the curve represents the change in velocity.

Graphs of SHM:

The graphs of displacement, velocity, and acceleration in SHM are all periodic functions (sine or cosine waves) and are 90° out of phase with each other. When displacement is maximum or minimum, velocity is zero. When displacement is zero (at the equilibrium position), velocity is maximum. Acceleration is always directed opposite to displacement and is maximum when displacement is maximum.

📸 Source/Description: Figure 4: This diagram shows how displacement, velocity, and acceleration change over time in simple harmonic motion. The graphs are periodic and have a 90-degree phase difference relative to each other.

Dynamics is the branch of physics that studies forces and how they affect the motion of objects.

3.1 Forces and Their Interactions (Newton's Laws)

Newton's laws of motion form the foundation of classical mechanics.

• First Law (Inertia): An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced external force. This law introduces the concept of inertia, the property of an object to resist changes in its state of motion.
• Second Law: The net force acting on an object is equal to the product of its mass and acceleration. This law also states that force is equal to the time rate of change of momentum.
• Third Law (Action-Reaction): For every action, there is an equal and opposite reaction. This means that if two objects interact, the force exerted by the first object on the second is equal in magnitude and opposite in direction to the force exerted by the second object on the first. This law is the basis for the law of conservation of momentum.

3.2 Examples of Forces

• Gravity (Weight): The gravitational force acting on an object near the Earth's surface. , where m is mass and g is the acceleration due to gravity (approx. 9.8 m/s²).
• Universal Gravitation: The attractive force between any two masses. , where G is the universal gravitational constant.
• Elastic Force (Hooke's Law): The restoring force exerted by an elastic object when it is deformed. , where k is the spring constant and x is the displacement from equilibrium.
• Friction: A force that resists the relative motion between two surfaces in contact. for static friction and for kinetic friction.
• Normal Force: The support force exerted by a surface on an object resting on it, acting perpendicular to the surface.

Free-Body Diagrams

Free-body diagrams are an essential tool for visualizing and analyzing all the external forces acting on an object. The object is represented as a single point, and the forces acting on it are drawn as vectors extending outwards from that point. This allows for a clear understanding of force balance and its effect on motion, even in complex situations.

📸 Source/Description: Figure 5: This free-body diagram shows the two main external forces acting on a book on a table: the upward normal force (F_norm) from the table and the downward force of gravity (F_grav) from the Earth.

3.3 Moment of Force and Center of Mass

• Moment of Force (Torque): A measure of the tendency of a force to cause or change the rotational motion of an object. , where F is the force, r is the moment arm (distance from the axis of rotation to the line of action of the force), and θ is the angle between the force vector and the moment arm. If the force acts perpendicularly, the formula simplifies to M = Fr.
• Moment of a Couple: The torque produced by two parallel forces that are equal in magnitude, opposite in direction, and not on the same line of action. , where F is the magnitude of one of the forces and d is the perpendicular distance between their lines of action.
• Condition for Rotational Equilibrium: For an object not to rotate, the sum of all torques acting on it must be zero: or .
• Center of Mass of a System of Particles: The position of the center of mass is the weighted average of the positions of the individual parts.

3.4 Impulse and Momentum

Momentum is the product of an object's mass and velocity. Impulse is the change in momentum.

• Momentum (p): A vector quantity given by , where m is mass and v is velocity.
• Impulse (I): The product of the force and the time over which it acts. Impulse is equal to the change in momentum.
• Impulse-Momentum Theorem: .
• Conservation of Momentum: In an isolated system (where the net external force is zero), the total momentum remains constant. This principle is particularly important in scenarios like collisions and explosions.

3.5 Advanced Dynamics: 2D Collisions & Coefficient of Restitution

In two-dimensional collisions, momentum is conserved independently along each axis (e.g., x and y).

The Coefficient of Restitution (e) quantifies the "bounciness" of a collision. It's the ratio of the relative speed of separation to the relative speed of approach.

• Perfectly Elastic Collision: . Kinetic energy is conserved.
• Inelastic Collision: . Kinetic energy is lost (usually as heat or sound).
• Perfectly Inelastic Collision: . The objects stick together after impact.

📸 Source/Description: Figure 6: An illustration of a 2D collision where momentum is conserved along both the x and y axes. The initial and final velocity vectors are resolved into their components.

3.6 Work, Energy, and Power

Work is done when a force causes a displacement. Energy is the capacity to do work. Power is the rate at which work is done.

• Work (W): Done when a force causes a displacement. , where F is force, d is displacement, and θ is the angle between them. The unit is the Joule (J).
• Kinetic Energy (KE): The energy an object possesses due to its motion. .
• Gravitational Potential Energy (GPE): Energy related to an object's position in a gravitational field. .
• Elastic Potential Energy (EPE): Energy stored in a deformed elastic object, like a spring. .
• Work-Energy Theorem: The net work done on an object equals the change in its kinetic energy ().
• Power (P): The rate at which work is done or energy is transferred. . The SI unit of power is the Watt (W).

Conservation of Mechanical Energy: If only conservative forces (like gravity, elastic force) act, the total mechanical energy (KE + PE) of a system is conserved. .

3.7 Advanced Energy: Non-Conservative Forces

When non-conservative forces like friction or air resistance are present, mechanical energy is not conserved. The work done by these forces () equals the change in the total mechanical energy of the system.

For example, the work done by friction is always negative, representing a loss of mechanical energy from the system, which is converted into thermal energy (heat).

Energy in Vertical Circular Motion

In vertical circular motion (e.g., a roller coaster loop), the tension or normal force changes with position because it must, along with gravity, provide the required centripetal force. Energy conservation is key to finding the speed at different points.

• At the top:
• At the bottom:

📸 Source/Description: Figure 7: Forces acting on a body in vertical circular motion. Tension and gravity contribute to the net centripetal force. Speed is greatest at the bottom and least at the top, governed by conservation of energy.

Fluid mechanics is the branch of physics that studies the properties and behavior of fluids (liquids and gases).

4.1 Fluid Properties and Behavior

• Fluid: A state of matter that yields to transverse or shear forces. Both liquids and gases are fluids.
• Density (ρ): Mass per unit volume. .
• Specific Gravity (s): The ratio of the density of a substance to the density of a reference substance, usually water. .

4.2 Hydrostatics (Fluids at Rest)

• Pressure (P): Force per unit area. . The SI unit is the Pascal (Pa).
• Pascal's Principle: A change in pressure applied to an enclosed, incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of the containing vessel. . Application: Hydraulic presses and car lifts.
• Stevin's Law (Hydrostatic Pressure): The pressure at a depth h in a fluid of constant density is given by . This law explains why pressure increases linearly with depth.
• Archimedes' Principle (Buoyant Force): The buoyant force on an object partially or fully immersed in a fluid is equal to the weight of the fluid that the object displaces. . This principle determines whether an object floats or sinks.

📸 Source/Description: Figure 8: This diagram shows a hydraulic system where Pascal's principle is applied. A force applied to a small piston is transmitted through the fluid, resulting in a larger amplified force on the larger piston.

📸 Source/Description: Figure 9: This diagram illustrates the concept of Archimedes' principle. An object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.

4.3 Fluid Dynamics (Fluids in Motion)

• Flow Rate (Q): The volume of fluid passing a certain point per unit time. .
• Continuity Equation: For an incompressible fluid, the mass flowing into a pipe must equal the mass flowing out. This is based on the principle that fluid cannot be created or destroyed as it flows. . Application: The speed of water increases when the nozzle of a garden hose is narrowed.
• Bernoulli's Equation: An application of the law of conservation of energy for an ideal fluid (non-viscous and incompressible). . This equation implies that as the speed of a fluid increases, its pressure decreases, and vice versa. Application: Explains how aircraft wings generate lift and the Venturi effect.

Thermodynamics is the branch of physics that deals with heat, work, and temperature, and their relation to energy.

5.1 Equilibrium, Temperature, and Heat Transfer

Thermal Equilibrium: When objects at different temperatures are in contact, heat flows from the hotter object to the colder one until they reach the same temperature. This state is thermal equilibrium.

Modes of Heat Transfer: Heat is primarily transferred in three ways:

• Conduction: Heat transfer through direct molecular collision. Occurs mainly in solids.
• Convection: Heat transfer through the bulk movement of fluids (liquids or gases).
• Radiation: Heat transfer via electromagnetic waves, which requires no medium.

📸 Source/Description: Figure 10: This diagram shows the three main modes by which heat is transferred between objects or through a medium: conduction, convection, and radiation.

5.2 Heat Capacity and Specific Heat

Specific Heat Capacity (c): The amount of heat energy required to raise the temperature of a unit mass of a substance by one degree. The heat required to change the temperature of a substance is given by:

5.3 Phase Change and Latent Heat

During a phase change, the temperature remains constant, and the heat absorbed or released is called latent heat.

Where L is the specific latent heat of fusion ( for melting/freezing) or vaporization ( for boiling/condensation).

5.4 Ideal Gas Law

The ideal gas law describes the relationship between the pressure, volume, temperature, and amount of an ideal gas.

Where P is absolute pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is absolute temperature (in Kelvin).

5.5 Laws of Thermodynamics

• First Law: A statement of the conservation of energy. The change in internal energy of a system equals the heat added to the system minus the work done by the system ().
• Second Law: This law states that the entropy (disorder) of an isolated system always increases or remains constant. It implies that heat spontaneously flows from hot to cold, and that no heat engine can be 100% efficient.

5.6 Advanced Thermodynamics: Ideal Gas Processes & Heat Engines

Understanding how an ideal gas behaves under different constraints is crucial. These processes are often visualized on a P-V (Pressure-Volume) diagram.

📸 Source/Description: Figure 11: A P-V diagram showing isobaric (horizontal), isochoric (vertical), isothermal (hyperbolic), and adiabatic (steeper hyperbola) processes.

The Carnot Cycle & Maximum Efficiency

The Carnot cycle is a theoretical thermodynamic cycle that gives the maximum possible efficiency for a heat engine operating between two temperatures.

Where is the absolute temperature of the cold reservoir and is the absolute temperature of the hot reservoir. No real engine can be more efficient than a Carnot engine.

📸 Source/Description: Figure 12: The Carnot cycle consists of two isothermal processes and two adiabatic processes, forming a closed loop on a P-V diagram.

A wave is a disturbance that transfers energy through a medium or space.

6.1 Wave Characteristics

• Frequency (f) and Period (T): . Unit is Hertz (Hz).
• Wavelength (λ): The spatial period of the wave.
• Wave Speed (v): The speed at which a wave propagates. .

6.2 Sound Waves and Doppler Effect

The Doppler effect is the change in frequency of a wave in relation to an observer who is moving relative to the wave source.

Where is observed frequency, is source frequency, is the speed of the wave in the medium, is the observer's speed, and is the source's speed.
(Top signs for "towards", bottom signs for "away").

6.3 Law of Refraction (Snell's Law)

Describes how light bends when passing between two different media.

Where are the refractive indices of the media and are the angles of incidence and refraction, respectively.

6.4 Advanced Optics: Interference, Diffraction, and Total Internal Reflection

Young's Double-Slit Experiment (Interference)

This experiment demonstrates the wave nature of light. When coherent light passes through two narrow slits, an interference pattern of bright and dark fringes is observed on a screen.

• Constructive Interference (Bright Fringes): Path difference is an integer multiple of the wavelength.
• Destructive Interference (Dark Fringes): Path difference is a half-integer multiple.

Where is the distance between slits, is the angle to the fringe, is the wavelength, and is an integer (the order number).

📸 Source/Description: Figure 13: Setup for Young's experiment. Light from a single source is diffracted by two slits, and the resulting waves interfere, creating a pattern of bright and dark bands on the screen.

Total Internal Reflection (TIR)

When light travels from a denser medium () to a less dense medium (), if the angle of incidence exceeds a certain critical angle (), the light is completely reflected back into the denser medium.

This principle is the basis for fiber optics.

📸 Source/Description: Figure 14: Light ray behavior at a boundary. Below the critical angle, refraction occurs. At the critical angle, the refracted ray is 90°. Above it, total internal reflection occurs.

This area studies electric charges, fields, currents, and magnetic fields, and their fundamental interactions.

7.1 Charge, Electric Field, and Potential

• Coulomb's Law: The force between two point charges. , where k is Coulomb's constant.
• Electric Field (E): The force per unit charge. . For a point charge: .
• Electric Potential (V): The potential energy per unit charge. . For a point charge: .

Relationship between E and V

The electric field is the negative gradient of the potential. In one dimension, this simplifies to the rate of change of potential with distance.

This means the electric field points in the direction of the steepest decrease in potential. Equipotential lines are always perpendicular to electric field lines.

📸 Source/Description: Figure 15: For a positive point charge, electric field lines radiate outwards, and equipotential lines are concentric circles. The field is stronger where the lines are closer together.

7.2 Capacitance and Capacitors

• Capacitance (C): The ability to store electric charge, defined as .
• Energy Stored in a Capacitor: .
• Capacitors in Series: .
• Capacitors in Parallel: .

7.3 Current, Resistance, and Ohm's Law

• Electric Current (I): The rate of flow of charge. .
• Resistance (R): Opposition to current flow. , where ρ is resistivity.
• Ohm's Law: .
• Resistors in Series: .
• Resistors in Parallel: .

7.4 Kirchhoff's Laws

• Current Law (Junction Rule): The sum of currents entering a junction equals the sum of currents leaving. .
• Voltage Law (Loop Rule): The sum of potential differences around any closed loop is zero. .

7.5 Electric Power

• Electric Power: .
• Joule Heating: Energy dissipated as heat in a resistor is .

7.6 Advanced E&M: RC Circuits & Magnetic Fields

RC Circuits (Transient Behavior)

An RC circuit contains a resistor and a capacitor. When a switch is closed, the capacitor doesn't charge or discharge instantaneously. This transient behavior is exponential.

• Time Constant (): The characteristic time for the circuit. . After one time constant, a capacitor charges to ~63% of its maximum value.
• Charging: and .
• Discharging: and .

📸 Source/Description: Figure 16: Voltage across the capacitor during charging (approaching max voltage) and discharging (decaying to zero). The time constant τ governs the speed of these exponential processes.

7.7 Magnetic Fields and Forces

• Magnetic Field Sources: Produced by moving charges (currents).
• Long Straight Wire:
• Center of a Circular Loop:
• Inside a Solenoid: (where n is turns per unit length).
• Lorentz Force: Force on a charge q moving with velocity v in a magnetic field B. . The direction is given by the right-hand rule.
• Force on a Current-Carrying Wire: .
• Electromagnetic Induction (Faraday's Law): A changing magnetic flux through a loop of wire induces an electromotive force (emf) or voltage.

Where N is the number of turns and is the magnetic flux. The negative sign (Lenz's Law) indicates the induced current creates a magnetic field that opposes the change in flux.

This advanced section explores the physics of the very small, where classical mechanics breaks down. A strong grasp here can be a key differentiator.

8.1 The Photoelectric Effect

This effect provided key evidence for the particle nature of light (photons). When light shines on a metal surface, electrons are ejected only if the light's frequency is above a certain threshold.

• is the maximum kinetic energy of the ejected electron.
• is Planck's constant.
• is the frequency of the incident light.
• is the work function of the metal (the minimum energy needed to remove an electron).

📸 Source/Description: Figure 17: A plot of maximum kinetic energy of photoelectrons versus light frequency. The slope of the line is Planck's constant (h), and the x-intercept gives the threshold frequency.

8.2 Atomic Models

Our understanding of the atom has evolved through several key models.

8.3 Radioactive Decay

The number of radioactive nuclei decreases exponentially over time according to the half-life.

Here, N(t) is the number of remaining nuclei, N₀ is the initial number of nuclei, t is the elapsed time, and T is the half-life.

Types of Radiation and Penetrating Power

• Alpha (α) Particles: Helium nuclei (). Low penetration (stopped by paper).
• Beta (β) Particles: High-energy electrons or positrons. Medium penetration (stopped by aluminum).
• Gamma (γ) Rays: High-energy photons (electromagnetic radiation). High penetration (requires thick lead or concrete).

📸 Source/Description: Figure 18: A diagram showing that alpha radiation is stopped by paper, beta radiation passes through paper but is stopped by aluminum, and gamma radiation passes through both but is attenuated by lead.

8.4 Mass-Energy Equivalence

Einstein's famous equation shows that mass and energy are interconvertible. This is the basis for the energy released in nuclear reactions.

Where E is energy, m is the mass defect (the change in mass during a nuclear reaction), and c is the speed of light in a vacuum.

Success in the IMAT Physics section requires mastering the fundamental formulas and concepts detailed in this report. Each area of physics is interconnected; for example, understanding vectors in kinematics is directly applicable to analyzing forces in dynamics and fields in electromagnetism. Recognizing the interrelationships between physical quantities and how they are constructed from base units enhances accuracy in problem-solving and fosters the flexibility to apply existing knowledge to new situations. Simply memorizing formulas is not enough; it is crucial to understand their derivation, scope of application, and the physical principles they represent to solve complex problems accurately. Regular review and application of these formulas to a variety of problems are recommended to strengthen both theoretical knowledge and practical problem-solving skills, which will cultivate the deep understanding and application abilities required for the IMAT Physics exam.