General Physics 1 Reviewer PDF

GENERAL PHYSICS 1 LE VERRIER SCIENCE CLUB REVIEWERS LESSON 1 | ROTATIONAL EQUILIBRIUM AND ROTATIONAL DYNAMICS Static Torque- Does not produce an angular accelera...

GENERAL PHYSICS 1 LE VERRIER SCIENCE CLUB REVIEWERS LESSON 1 | ROTATIONAL EQUILIBRIUM AND ROTATIONAL DYNAMICS Static Torque- Does not produce an angular acceleration MOMENT OF INERTIA Dynamic Torque- Does not produce an angular The opposition that the body exhibits to acceleration having its speed of rotation about an axis altered by the application of a torque (turning force) Moment of inertia of the body depends upon the mass of the body, axis of rotation of the body and shape and size of the body. Formula of Moment of inertia: I = MR I- inertia M-Mass R- Radius How is Torque calculated? If r is perpendicular to F, then torque Moment of inertia of various regular object can be τ = rF calculated: If r is not perpendicular to F, then torque τ = rF sin θ θ = is the angle between r (moment of arm) and F (force vector) r = the length of an arm (distance) in meters (m) F = force exerted in Newton (N) How is Torque measured? SI unit for torque is the Newton-meter. mailto:https://www.ck12.org/book/peoples-physics-c (Nm) oncepts/section/9.2/ ROLE OF TORQUE PLAY IN RATIONAL KINEMATICS TORQUE TORQUE Torque takes the place of force in linear kinematics. A measure of the force that can cause an There is a direct equivalent to Newton’s 2nd law of object to rotate about an axis. motion. F = ma Causes an object to acquire angular τ =Iα acceleration. α is the angular acceleration I is the rotational inertia Torque is a Vector quantity, the direction of the torque vector depends on the direction of ANGULAR ACCELERATION the force on the axis. Rate of change of angular velocity with a time TWO TYPES OF TORQUE of an object in motion. Acceleration is the LE VERRIER | 1  GENERAL PHYSICS 1 LE VERRIER SCIENCE CLUB REVIEWERS change in velocity of a moving object with respect to time. If the object moves on a When this happens, this can mean that there circular direction then its velocity is called is no torque acting on the object, or all the angular velocity. torques acting on the object are canceling each other out. The larger I, the harder it is for an object to acquire angular acceleration. LESSON 2 | GRAVITY GRAVITY EQUILIBRIUM Gravity is a force of attraction that exists between any two masses, any two bodies, When all the forces that act upon an object any two particles. are balanced, then the object is said to be in It is an attraction that exists between all a state of equilibrium. objects, everywhere in the universe. Sir Isaac Newton (1642-1727) Sir Isaac Newton theorized the Law of Gravitation in 1687. Discovered that a force (gravity) is required to change the speed or direction of movement of an object. NEWTON’S LAW OF UNIVERSAL GRAVITATION mailto:https://www.physicsclassroom.com/class/vect ors/Lesson- 3/Equilibrium-and-Statics ALL objects attract each other with a force of EQUILIBRIUM=BALANCED gravitational attraction. Static Equilibrium This force of gravitational attraction is directly An object is at rest and is in a state of dependent upon the masses of both objects equilibrium, then we would say that the object and inversely proportional to the square of is at "static equilibrium." the distance that separates their centers. Formula: Rational Equilibrium The concept of rotational equilibrium is an equivalent to Newton’s 1st law for a rotational system. An object which is not rotating remains not rotating unless acted on by an G- Universal gravity (6.673 X10-11 𝑁𝑚2/𝑘𝑔2) external torque. m1m2- mass (kg) r - distance (m) Total T = T{1} + T{2} +...+ T{n} F- force (N) In this equation, n is the total number of Difference between G and g. torques being applied to the object. G- Universal gravity (6.673 X10-11) g- Acceleration due to gravity ( 9.8 m/𝑠2) In this case, If the addition of all the torques acting on an object equals zero. This is called “rotational GRAVITATIONAL FIELD equilibrium.” LE VERRIER | 2  GENERAL PHYSICS 1 LE VERRIER SCIENCE CLUB REVIEWERS A gravitational force per unit mass that would similar to an oval. For the planets, the orbits be exerted on a small mass at that point are almost circular. The pattern of gravitational field of the Earth can be represented by arrows and known as The orbits of comets have a different shape. field lines. They are highly eccentric or "squashed." They When these field lines are closest together, look more like thin ellipses than circles. the gravitational field is strongest. Hence, the distance between the lines is inversely Satellites that orbit Earth, including the moon, do not proportional to the field strength. always stay the same distance from Earth. Sometimes they are closer, and at other times they are farther away. mailto:https://commons.wikimedia.org/wiki/File:Gravit ational_field_Earth_lines.svg mailto:https://www.pbs.org/newshour/science/catch -the-supermoon-lunar-eclipse-heres-what-you-saw Perigee - Closest point a satellite comes to Earth. Apogee - Farthest point a satellite comes to Earth. Gravitational Potential Energy Perihelion - A planet’s point in their orbit closest to the The energy stored in an object as the result of sun. its vertical position or height. The energy is Aphelion - A planet’s point in their orbit Farthest to stored as the result of the gravitational the sun. attraction of the Earth for the object. ORBITS KEPLER’S MOTION LAW OF PLANETARY MOTION It is a regular, repeating path that one object JOHANNES KEPLER (1571-1632) in space takes around another one. German astronomer who discovered three major An object in an orbit is called a satellite. laws of planetary motion. Natural satellite- earth, moon Man-made satellite- International Space station KEPLER’S FIRST LAW PLANETS MOVE IN ELLIPTICAL ORBITS WITH THE SUN AS A Orbits come in different shapes. All orbits are FOCUS elliptical, which means they are an ellipse, Distance between the planet and sun is LE VERRIER | 3  GENERAL PHYSICS 1 LE VERRIER SCIENCE CLUB REVIEWERS constantly changing as the planet orbits around the sun. Formula: 𝐓=𝟏/𝐅 KEPLER’S SECOND LAW ANGULAR FREQUENCY A PLANET COVERS THE SAME AREA OF SPACE IN THE SAME AMOUNT OF TIME NO MATTER WHERE IT IS IN ITS Represented by the Greek letter ω (omega). ORBIT Refers to the angular displacement per unit Planet’s area of space in same amount of time or; time is still the same no matter where it is in its orbit. The rate of change of the phase of a However, the speed of the planet varies on how sinusoidal waveform or; close/far the planet is in the sun. Rate of change of the argument of the sine function. Perihelion (nearest) = Fastest Aphelion (farthest) = Slowest Formula: 𝛚 = 𝟐𝛑𝒇 KEPLER’S THIRD LAW ω = Angular frequency F = frequency A PLANET’S ORBITAL PERIOD IS PROPORTIONAL TO THE π = 3.14 (Pi) SIZE OF ITS ORBIT (ITS SEMI-MAJOR AXIS). Angular frequency is often represented in units of If the size of an orbit is small, then its Orbital radians per second (there are 2π radians in a circle) period is short. Ex. Mercury (closest to the SI Unit : rad/s sun) Orbital period: 88 days RESTORING FORCE LESSON 3 | PERIODIC MOTION The restoring force causes an oscillating PERIODIC MOTION object to move back toward its stable equilibrium position, where the net force on it PERIODIC MOTION is zero. A motion repeated in equal intervals of time. Period - Interval of time for a cycle of motion. Oscillatory - A motion in which the body moves to and from about a fixed position. Frequency - The number of periods per unit time or the number of complete cycles each second. Measured in Hertz (Hz). Formula: 𝒇=1/𝐓 mailto:https://courses.lumenlearning.com/suny-phys F= frequency (“Hz” for hertz) ics/chapter/16-1-hookes-law-stress-and- T= time period ( “s” for seconds) strain-revisited/ TIME PERIOD - Period of time it takes to get back to The simplest oscillations occur when the where it started whatever the motion may be. restoring force is directly to displacement. In LE VERRIER | 4  GENERAL PHYSICS 1 LE VERRIER SCIENCE CLUB REVIEWERS this case the force can be calculated as, 3 MAIN TYPES OF MECHANICAL WAVES F=−kx TRANSVERSE WAVE F = restoring force - Particles of the medium vibrate up and down k = force constant perpendicular to the direction of the wave. x = displacement - A wave that causes the medium to vibrate at right angles to the direction in which the The motion of a mass on a spring can be wave travels. described as Simple Harmonic Motion (SHM): oscillatory motion that follows Hooke’s Law. SIMPLE HARMONIC MOTION A type of periodic motion where the restoring force is directly proportional to the displacement. SINGLE PENDULUM An object that has a small mass, also known as the pendulum bob, which is suspended from a wire or string of negligible mass. Pendulum will oscillate around its equilibrium mailto:https://www.vedantu.com/question-answer/a point due to momentum in balance with the -explain-the-terms-crests-and-troughs-of- restoring force of gravity when displaced. a-wave-class-11-physics-cbse-60b4d7b198693b78c6 1e0596 PHYSICAL PENDULUM Generalized case of the simple pendulum. It Crest - a wave is the point on the medium that consists of any rigid body that oscillates exhibits the maximum amount of positive or upward about a pivot point. displacement from the rest position. For small amplitudes, the period of a physical Trough - a wave is the point on the medium that pendulum only depends on the moment of exhibits the maximum amount of negative or inertia of the body around the pivot point and downward displacement from the rest position. the distance from the pivot to the body’s center of mass. LONGITUDINAL WAVE ➔ However, it is not independent of the mass A wave in which the vibration of the medium distribution of the rigid body. A change in is parallel to the direction the wave travels. shape, size, or mass distribution will change the moment of inertia and thus, the period. LESSON 4 | MECHANICAL WAVES AND SOUND MECHANICAL WAVE - A wave that is an oscillation of matter, and therefore transfers energy through a medium. mailto:https://byjus.com/physics/longitudinal-wave/ COMPRESSION An area where the particles in a medium are LE VERRIER | 5  GENERAL PHYSICS 1 LE VERRIER SCIENCE CLUB REVIEWERS spaced close together. Speed = Wavelength x Frequency Has the maximum density v=λ 𝐱 υ SI Unit REFRACTION Speed = m/s An area where the particles in a medium are Wavelength = m spread out. Frequency = 1/s or Hz Has the minimum density. PERIODIC WAVE A wave with a repeating continuous pattern SURFACE WAVE which determines its wavelength and A wave that travels along a surface frequency. separating two media. In a surface wave, particles of the medium SINUSOIDAL OR SINE WAVE - A CONTINUOUS WAVE vibrate both up and down and back and forth, - Curve that describes a smooth repetitive so they end up moving in a circle. oscillation. BEHAVIOR OF WAVES REFLECTION Reflection occurs when a wave bounces off a surface that is cannot pass through. PROPERTIES OF MECHANICAL WAVES FREQUENCY The number of complete cycles in a given time. AMPLITUDE REFRACTION The amplitude of a wave is the maximum Refraction is the bending of a wave as it displacement of the medium from its rest enters a new medium at an angle. position. WAVELENGTH Distance between a point on one wave and the same point on the next cycle of the wave. SPEED Waves are traveling at a constant speed, then wavelength is inversely proportional to frequency. WAVE SPEED DIFFRACTION Formula for wave speed: Diffraction is the bending of a wave as it LE VERRIER | 6  GENERAL PHYSICS 1 LE VERRIER SCIENCE CLUB REVIEWERS moves around an obstacle or passes through Intensity is the rate at which a wave’s energy a narrow opening. flows through a given area. FREQUENCY AND PITCH Pitch is the frequency of a sound as you perceive it. High-frequency → high pitch Low- frequency →low pitch. THE DOPPLER EFFECT INTERFERENCE A change in sound frequency caused by Interference occurs when two or more waves motion of the sound source, motion of the overlap and combine together. listener, or both. ➔ Sound source approaches, an observer hears Constructive Interference - occurs when two a higher frequency. or more waves combine to produce a wave ➔ Sound source moves away, the observer with a larger displacement. hears a lower frequency. Destructive Interference - occurs when two or more waves combine to produce a wave LESSON 5 | FLUID MECHANICS with a smaller displacement. UNDERSTANDING FLUIDS DEFINITION OF FLUID - Fluids are substances that flow and change shape under the influence of external STANDING WAVES force. A standing wave is a wave that appears to stay in one place. DENSITY An important characteristic of substances. It SOUNDS is crucial, for example, in determining whether an object sinks or floats in a fluid. Sound is a mechanical wave that results from Density is the mass per unit volume of a the back-and-forth vibration of the particles substance or object. of the medium through which the sound wave is moving. MASS DENSITY ➔ Sound waves are longitudinal waves that Defined as the mass per unit volume of travel through a medium. substance. Denoted by the Greek Letter rho (ρ) Formula: BEHAVIORS OF SOUND ρ = m/V SPEED ρ : Density (in kg/m3) In dry air at 20°C, the speed of sound is 342 m/s. m : Mass (in kg) In general, sound waves travel fastest in solids, slower in liquids, and slowest in gases. V : Volume (in m3) INTENSITY AND LOUDNESS BUOYANCY LE VERRIER | 7  GENERAL PHYSICS 1 LE VERRIER SCIENCE CLUB REVIEWERS Measure of the upward force a fluid exerts on Incompressible Fluid - The fluid density is constant an object that is submerged. throughout. ➔ A Greek mathematician named Archimedes Laminar Flow - The fluid moves smoothly without realized that buoyant force is equal to the turbulence. weight of fluid displaced by an object. Low Viscosity - Minimal resistance within the fluid. ARCHIMEDES’ PRINCIPLE EQUATION OF CONTINUITY States that the buoyant force on an object is equal to the weight of the fluid displaced by The mass flow rate at one point in the pipe will the object.: be equal to the mass flow rate at any other FORMULA: point. 𝑭𝑩 = 𝒎𝑭𝒈 ∆𝒎𝟏/∆𝒕 = ∆𝒎𝟐/∆𝒕 Where, 𝐹𝐵 = buoyant force 𝑚𝐹 = mass of displaced fluid g = force of gravity -9.81m/𝑠2 PASCAL’S PRINCIPLE states that in a fluid at rest in a closed container, a pressure change in one part is “The distance the fluid moves, divided by the transmitted without loss to every portion of change in time, is equal to the fluid’s velocity.” the fluid and to the walls of the container. ➔ By putting that all together, you can get a To calculate the pressure of a fluid at a given depth: different version of the equation of continuity: P=ρgh 𝝆𝟏𝑨𝟏𝑽𝟏 = 𝝆𝟐𝑨𝟐𝑽𝟐 Wherein: P = pressure g = gravity ρ = density h = height Pressure as applied force divided by area is: P=F/A It is measured in units of Newtons per meters squared, known as Pascal: 1 N/𝑚2= 1 Pa BERNOULLI'S PRINCIPLE BERNOULLI'S PRINCIPLE “The higher the fluid’s velocity is through a Fluids are incompressible, have laminar flow pipe, the lower the pressure on the pipe’s (flows smoothly) and low in viscosity. walls, and vice versa. KEY ASSUMPTIONS 𝐏 + 𝟏/2 𝛒𝐕2 + 𝝆𝐠𝐲 = a constant LE VERRIER | 8  GENERAL PHYSICS 1 LE VERRIER SCIENCE CLUB REVIEWERS Type of energy that can come from where LESSON 6 | LAWS OF THERMODYNAMICS something is, even if it’s not moving, like a stored energy. THERMODYNAMICS Branch of physics and engineering that INTERNAL ENERGY (U) focuses on converting energy, often in the Energy associated with the seemingly random movement of molecules. form of heat and work. Describes how thermal energy is converted to Energy that can move between boundaries: and from other forms of energy and to work. A. Heat (Q) – which is the flow of thermal energy. B. Work (W) – which is essentially any type of energy ZEROTH LAW OF THERMODYNAMICS other than heat. “When two objects are individually in thermal equilibrium with a third object, then they are THE SECOND LAW OF THERMODYNAMICS also in equilibrium with each other.” During the process of energy transfer or transformation there will be a disorder in the CALORIMETRY enclosed system. It is a study which determines the changes of ➔ ‘disorder’ is called Entropy. energy (heat) in a system by measuring the Causes energy loss during heat transfer usually in the form of heat dissipation, among heat exchanged with the surroundings. many others. Allows the natural tendency of any isolated THE FIRST LAW OF THERMODYNAMICS system to degenerate into a more disordered state. Heat as a form of energy, which means it can neither be created nor destroyed, but can be CLAUSIUS STATEMENT converted. For any process, a natural flow of energy will always be from higher energy value to lower Energy inside the system: energy value. Hotter objects naturally give off heat to the KINETIC ENERGY (KE) colder body until it reaches thermal The type of energy that’s involved with equilibrium. movement. In some cases, this process can be reversed without breaking the Laws of Translational kinetic energy - the most common form Thermodynamics using 'Heat Pumps' of energy and is when something moves from one (Refrigeration) location to another. In heat pumps, there are major components Rotational kinetic energy - when something spins or to complete the refrigeration cycle. In those rotates. components, the Evaporator is responsible for absorbing heat from the food inside the Vibrational kinetic energy - when something shakes refrigerator. Meanwhile, Condenser is a and vibrates. component that removes heat from the refrigerant to cool the fridge. POTENTIAL ENERGY (PE) LE VERRIER | 9  GENERAL PHYSICS 1 LE VERRIER SCIENCE CLUB REVIEWERS KELVIN-PLANCK STATEMENT It is impossible for a system to accept a given amount of heat from a high FOUR TYPES OF THERMODYNAMIC PROCESSES temperature medium and to deliver an equal ISOBARIC PROCESS amount of work output. A thermodynamic process changes the state There will always be energy losses during the of a certain amount of matter in which the process pressure remains constant. ENTROPY STATEMENT ADIABATIC PROCESS The total entropy of a system either increases A process without transfer of heat to or from a or remains constant in any spontaneous system, so that Q = 0. process, it never decreases. Process in which there is no heat transfer It is impossible for any system to operate in a involved. way that entropy is destroyed. Adiabatic Heating occurs when the pressure of a gas is increased by work done on it by its Surroundings. THE THIRD LAW OF THERMODYNAMICS Entropy of any crystalline substance at ISOCHORIC PROCESS absolute zero will be equal to zero. Thermodynamic process in which the volume ➔ When an object’s (an enclosed system) remains constant. temperature lowers, the kinetic energy also The ideal Otto cycle is an example of an lowers until it reaches a state where there will isochoric process be no more temperature (kinetic/heat With no change in volume, dV=0, there can be energy). This is called Absolute Zero. no work done on or by the gas. The value of absolute zero is 0 Kelvin (K) or -273.15°C. ISOTHERMAL PROCESS At absolute zero, every substance is in a solid Process that occurs under constant phase. temperature but other parameters of the system can be changed accordingly. ENTHALPY Temperature remains constant. Measurement of total energy in an isolated thermodynamic system. THERMAL EXPANSION AND VOLUME EXPANSION Amount of enthalpy can be calculated by finding the total heat of a system, equivalent Object expands and becomes larger due to a to the system internal energy plus volume change in its temperature. and pressure. Thus we can say that when a solid body is expanding, the increase in length is ➔ Entropy and Enthalpy are both State dependent upon three factors: Functions, it means that both are defined by their initial and end (final) states. On heating a rod the increase in its length ➔ Depends on the material of the rod. THERMODYNAMIC PROCESS ➔ Is directly proportional to its original length. ➔ Is directly proportional to the increase in its Change from initial state to a final state of a temperature. system that usually involves a change in its pressure, volume, or temperature. LE VERRIER | 10  GENERAL PHYSICS 1 LE VERRIER SCIENCE CLUB REVIEWERS FORMULA FOR THERMAL EXPANSION TYPES OF COMBUSTION ENGINE INTERNAL COMBUSTION ENGINE A type of combustion engine in which the fuel is burnt inside the system. 𝐿𝑜 = initial length of the rod Uses fossil fuels such as Gasoline, Diesel, and 𝐿𝑡 = length when the rod expands Bunker fuels as their prime mover (fuel). 0°C = the temperature at the initial t°C = rise in temperature EXTERNAL COMBUSTION ENGINE 𝐿𝑡 - 𝐿𝑜 = the thermal expansion of the rod A type of combustion engine in which the α = the coefficient of thermal expansion (proportional combustion takes place outside the system. constant) It usually uses coal, biomass, and other types IDEAL GAS LAW of fuels as their prime mover. Defined as one in which all collisions between THERMAL EFFICIENCY atoms or molecules are perfectly elastic hence, there is no intermolecular attractive They measure how useful a system or engine forces between these atoms/molecules. utilizes heat based on its input and work PV = nRT = NkT output. n = Number of moles The more heat converted into work, the more R = Universal gas constant = 8.3145J/mol·K N = Number of molecules efficient an engine is. k = Boltzmann constant = 1.38066x10-23 J/K Qc Formula: T = Temperature in Kelvin 𝑾 = 𝐐𝐡 − 𝐐𝐜 Thermal efficiency formula: 𝐖 = 𝐐𝐡−𝐐𝐜/𝐐𝐡𝐗𝟏𝟎𝟎 HEAT ENGINE Produces motion by transforming heat into mechanical energy. REVERSIBLE AND IRREVERSIBLE PROCESS LE VERRIER | 11  GENERAL PHYSICS 1 LE VERRIER SCIENCE CLUB REVIEWERS REVERSIBLE PROCESS Is a thermodynamic process that can be turned back into their original states. Example of a reversible heat engine is the Carnot Engine IRREVERSIBLE PROCESS Defined as a process in which the system and the surroundings do not return to their original condition once the process is initiated. TEMPERATURE Is a physical quantity that expresses hot and cold. ➔ Temperature is measured with a thermometer. The most common scales are: Celsius scale - Formerly called centigrade, denoted as °C. Fahrenheit scale - denoted as °F Kelvin scale - denoted as K, predominantly used for scientific purposes by conventions of the International System of Units (SI). The lowest theoretical temperature is absolute zero, at which no more thermal energy can be extracted from a body. LE VERRIER | 12