Gen Physics Past Paper PDF

GEN PHYSICS SEM 1 | QUARTER 2 | alyssa – ♡ cramer L1 MOMENT OF INERTIA & TORQUE ★ TORQUE - Produced by this turning force and tends to produce rotational acceleration - A measure of how much force is acting on an object causing it to rotate...

GEN PHYSICS SEM 1 | QUARTER 2 | alyssa – ♡ cramer L1 MOMENT OF INERTIA & TORQUE ★ TORQUE - Produced by this turning force and tends to produce rotational acceleration - A measure of how much force is acting on an object causing it to rotate ★ ANGULAR MOMENTUM Things that rotates, whether a colony in space, a cylinder rolling down an incline, or an acrobat doing a somersault, remain rotating until something stops them. A rotating object has an inertia of rotation. - “Inertia of rotation” of rotating objects - Moment of inertia: name given to rotational inertia ★ Factors affecting torque - The moment of inertia in rotational - Pivot point (θ): Axis where the object rotates motion is analogous to mass in - Moment arm/Lever arm (R): Distance from the translational motion pivot to the point where the force acts - An object is said to be in rotational - Force (F): Force applied on the object equilibrium when there is no net torque - Angle: In between the position of vector R and acting on the object force (F) vector - Central gravity: Where the mass is concentrated Formulas ★ Types of torque Moment of inertia a. Static torque: does not produce angular acceleration b. Dynamic torque: produces angular acceleration Point objects ★ Sign conventions Angular momentum = linear momentum x radius of its circular path Rigid objects Angular momentum = moment of inertia x angular velocity - Torque is positive if its rotation is a counterclockwise direction - Torque is negative if it rotates clockwise direction L2 ANGULAR MOMENTUM Formula Unit: newton-meter (N.m) ★ EQUILIBRIUM - Condition where there is no change in the state of motion 1 GEN PHYSICS SEM 1 | QUARTER 2 | alyssa – ♡ cramer - The body is either at rest or moving with constant ★ Angular acceleration: the angular velocity changes velocity in the same direction ★ Conditions for equilibrium Formula 1. The net external force of the system must be zero, therefore the net external force in any direction is Angular velocity zero Fnet = 0, (no net force) ∑Fx = 0; ∑Fy = 0 2. The net external torque of the system must be zero, therefore the net external torque in any direction is zero, τnet = 0, (no net torque) ∑τclockwise = 0 ; ∑τcounter clockwise = 0 Angular acceleration ★ Force systems L3 TORQUE-ANGULAR MOMENTUM RELATION - Torque showed that it is the result of applying a force at a distance from the axis of rotation - The angular momentum of a rotating object has a symbol L, and it is the result of linear momentum at a Concurrent forces distance from the axis of rotation - Forces acting on a common point, thus, the body - Torque is the rotational equivalent of force and does not rotate - Angular momentum is the rotational equivalent of - A particle or a point mass experience concurrent translational momentum forces - Just as the moment of inertia was analogous to mass, the angular momentum in rotational motion is Non-concurrent forces analogous to the momentum of an object for - Forces acting on different points on a body causing translational motion it to rotate ↳ Torque is the rate of change of angular - Occurs in a rigid body or extended body that does momentum. not change size and shape. L4 NEWTON’S LAW OF UNIVERSAL GRAVITATION ★ Conservation of Angular Momentum ★ NEWTON’S LAW OF GRAVITATION - States that any two objects in the universe attract one “If no external force acts on a rotating system, the angular another with a force proportional to the product of momentum of that system remains constant” their masses m1 and m2 - The force is inversely proportional to the square of Terminologies the distance d between them. ★ Angular velocity: the rate of change of angle 2 GEN PHYSICS SEM 1 | QUARTER 2 | alyssa – ♡ cramer ★ NEWTON’S LAW OF GRAVITATION - Is equal to the work needed to move an object to that location from a fixed reference location. States that any two objects in the universe attract one another with a force proportional to the product of their Formula masses m1 and m2 - The force is inversely proportional to the square of Gravitational potential energy NEAR the Earth’s the distance d between them surface - Although Newton gave his theory in the 17th century, it took 150 years to find the value of G. ↳ Finally, the English Physicist Henry Cavendish accomplished this using a torsion balance and found the value of the gravitational constant Gravitational potential energy FARTHER the Earth’s surface Terminologies ★ Angular velocity: the rate of change of angle ★ Angular acceleration: the angular velocity changes Formula ★ ESCAPE VELOCITY - The minimum velocity required for an object to escape completely from the gravitational field of a planet Formula Gravitational constant Escape velocity or Escape velocity for celestial objects near the Earth L5 GRAVITATIONAL POTENTIAL ENERGY, ESCAPE VELOCITY, & SATELLITE MOTION ★ GRAVITATIONAL POTENTIAL ENERGY & ESCAPE ★ SATELLITE MOTION VELOCITY - Many artificial satellites have nearly circular orbits. 3 GEN PHYSICS SEM 1 | QUARTER 2 | alyssa – ♡ cramer - Centripetal force must be present to keep this - Point at which the planet is close to the sun satellite moving in a circle. - About 147 million kilometres from the sun - The earth’s gravitational force provides the Centripetal force and keeps the satellite moving in Aphelion a circle - Point at which the planet is farther from the sun - 152 million kilometres from the sun Formula Period of circular orbit L6 KEPLER’S LAW OF PLANETARY MOTION [Summary of narrative] Kepler's First Law, which states that planets orbit in ellipses, ★ KEPLER’S LAW OF PLANETARY MOTION faced resistance due to the belief in the perfection of circular orbits in celestial spheres. Despite this, Kepler's law was History supported by observational data, and since its publication, - Astronomy began to establish as an exact science both natural and artificial satellites have been shown to follow with the detailed and accurate observations of elliptical orbits Tycho Brahe - For more than 20 years, Brahe kept detailed records of the positions of the planets and stars - In 1600, Brahe invited Kepler to be one of his ★ Kepler’s second’s law: Law of equal areas assistants. The following year, Brahe died “The radius vector drawn from the sun to the planet sweeps suddenly, leaving all of his detailed data to Kepler out equal areas in equal intervals of time” - By trial and error, Kepler discovered three empirical relationships that describe the motion - As the orbit is not circular, the planet’s kinetic of the planets – These relationships are known energy is not constant in its path today as Kepler’s laws of planetary motion. - It has more kinetic energy near the perihelion - Less kinetic energy near the aphelion Kepler’s Law - Since the arcs close to the Sun (perihelion) are 1. Planets move in elliptical orbits, with the Sun at longer than the arcs more distant from the Sun one focus of the ellipse. (aphelion), the planet must be moving more rapidly 2. An imaginary line between the Sun and a planet when it is close to the Sun (perihelion) sweeps out equal areas in equal time intervals. - Planet at perihelion moves faster; Planet 3. The quotient of the square of the period of a at aphelion moves slower planet’s revolution around the Sun and the cube of - The same length of time was needed for a planet the average distance from the Sun is constant and to move along each of the arcs at the ends of the the same for all planets segments of the ellipse. ★ Kepler’s first law: Law of ellipses or orbits “All the planets revolve around the sun in elliptical orbits having the sun at one of the foci” Perihelion 4 GEN PHYSICS SEM 1 | QUARTER 2 | alyssa – ♡ cramer object and works in the opposite direction of it Kepler did not know why planets moved faster when they were close to the Sun and slowly when they were farther away.* - The spring force always pushes or pulls the mass toward its original equilibrium position. For this ★ Kepler’s third law: Law of periods reason, it is sometimes called a restoring force ↳ Equilibrium position: The position “The square of the time period of revolution of a planet present in any spring of natural length at around the sun in an elliptical orbit is directly proportional to which exerts no force on mass the cube of its semi-major axis” - The shorter the orbit of the planet around the sun, ★ TERMS IN VIBRATIONAL MOTION the shorter the time taken to complete one revolution. [Summary of narrative] Kepler didn’t understand the significance of this constant. It wasn't until Newton's Law of Universal Gravitation that the relationship between the Sun’s gravity and planetary motion was understood. Newton’s theory explained how gravity causes the planets’ motion and provided the mathematical connection to Kepler's law, with the constant linked to gravitational forces. - Displacement: distance x of the mass from the equilibrium point at any moment Formula - Amplitude: maximum displacement – the greatest distance from the equilibrium point Period of circular orbit - Cycle: refers to the complete to- and-fro motion from one initial point back to that same point - Period: defined as the time required to complete one cycle - Frequency: the number of complete cycles per second. L7 SIMPLE HARMONIC MOTION ★ SINUSOIDAL MOTION ★ SIMPLE HARMONIC MOTION - Special kind of periodic motion where the restoring force depends directly on the displacement of the 5 GEN PHYSICS SEM 1 | QUARTER 2 | alyssa – ♡ cramer - Waves that vibrate parallel to the direction of motion of the wave - Compressions: regions where waves are closer together in a longitudinal wave - Rarefactions: regions where they are farther apart - Ex. slinky springs and the waves can be produced by Formula moving one end of the spring back and forth in the direction of its length Simple harmonic motion 2. Transverse wave Mass on the spring Simple pendulum - Particles in a medium vibrate at right angles Physical pendulum (perpendicular) to the direction in which the wave travels such as water waves and waves in a rope - Crest: positive pulse; highest part - Trough: negative pulse; lowest part ★ SINUSOIDAL WAVE - Sine or sinusoidal wave is a curve that describes a L8 MECHANICAL WAVE smooth repetitive oscillation - A waveform in which the amplitude is always proportional to the sine of its displacement angle ★ MECHANICAL WAVE at every point of time - Produced when particles vibrate in a medium in which the wave propagates - As a result, the momentum and energy are exchange among the particles and the medium - Can propagate through solid, liquid, or gas TYPES OF MECHANICAL WAVE 1. Longitudinal wave ★ HARMONIC OSCILLATOR - A system when displaced from its equilibrium 6 GEN PHYSICS SEM 1 | QUARTER 2 | alyssa – ♡ cramer position experiences a restoring force, F, and is proportional to the displacement, x 1.Simple harmonic oscillator - F is the only force acting on the system and undergoes simple harmonic motion which is made up of sinusoidal oscillations about the equilibrium point, with a constant amplitude and constant frequency. 2. Damped harmonic oscillator - When a frictional force is proportional to the velocity and is present in the harmonic oscillator - If the coefficient of friction is present, the system will undergo L9 SUPERPOSITION OF WAVES ↳ Underdamped harmonic oscillator: Oscillation with a frequency smaller than the non-damped case and has a ★ SUPERPOSITION OF WAVES decreasing amplitude with respect to time ↳ Overdamped harmonic oscillator: Decay “The displacement of a medium caused by two or more in its equilibrium position without waves is the algebraic sum of the displacements caused oscillations by the individual waves” Y = Y1 + Y2 3. Critically damped oscillator Y = displacement of the wave - Between the underdamped and overdamped oscillator case and occurs at a particular value of the coefficient of friction ★ INTERFERENCE 4. Driven oscillator - The result of superposition of two or more waves - if an external force is present which is dependent on time Types of interference 1. Constructive interference ★ WAVE EQUATION - It describes not only the movement of strings and wires, but also the movement of fluid surfaces, e.g., water waves - When two or more waves interfere to Since v = Δd/Δt produce a resultant displacement greater And Δd = λ and Δd = T than the displacement that is caused by Substituting: v = λ/T either wave Therefore: v = fλ 2. Destructive interference ★ INVERSE SQUARE LAW - The intensity or brightness of light as a function of the distance from the light source follows an inverse square relationship. - When the resultant displacement is smaller than the displacement that would be caused by one wave 7 GEN PHYSICS SEM 1 | QUARTER 2 | alyssa – ♡ cramer ★ PHASE ★ DOPPLER EFFECT - Refers to the relative position of the waves’ crest - Doppler effect in physics is defined as the increase (highest point of a wave) (or decrease) in the frequency of sound, light, or other waves as the source and observer move towards (or away from) each other. L10 FLUID MECHANICS ★ FLUID MECHANICS - The study of fluid properties - Hydrostatics/fluid statics: deals with fluids at rest - Hydrodynamics/fluid dynamics: deals with fluids in motion - When the crests and troughs are ALIGNED for constructive interference the two waves are in Mass density phase - A property of matter defined as the ratio of its ↳ Has a phase difference of 0 degrees or mass (m) to its volume (V) multiples of 360 degrees - Denoted by the Greek letter rho (ρ) - When the crest of one wave REPEATEDLY MEET troughs of the other wave in destructive interference, they are completely out of phase ↳ Waves are out of phase by 180 degrees or odd multiples (ex. like 540 degrees) ★ STANDING WAVE Density of solid - To determine the density of a solid, one needs to - The nodes and antinodes are stationary. The wave know its mass and volume appears to be standing still - The mass of a solid may be determined by using - If you double the frequency of vibration, you can a weighing scale produce additional nodes on the rope - For regular-shaped objects, the volume may be - Further increases in frequency produce even more determined from their dimensions nodes - For regular-shaped objects, the volume may be - The frequencies at which standing waves are determined from their dimensions produced are the natural frequencies or resonant - Displacement method: object is frequencies of the cord, and the different standing dipped into a container with liquid wave patterns are “resonant modes of vibration” Density of liquid - The density of a liquid is usually determined by 8 GEN PHYSICS SEM 1 | QUARTER 2 | alyssa – ♡ cramer ★ PASCAL’S PRINCIPLE using a bottle called a pycnometer - Pycnometer: It is weighted (in terms of Any change in pressure in an enclosed fluid at rest is mass) twice transmitted completely to all parts of the fluid 1. When it is empty and 2. When it is filled with a given liquid. The mass of the liquid Formula is the difference between the two masses. Pressure - Defined as the magnitude of the force acting perpendicular per unit area of the surface Hydrostatic pressure - The force per unit area that a confined liquid exerts on all parts of its container or any part of the object immersed in it - The forces exerted by the liquid are perpendicular to the walls of the container - The pressure on a given point in the liquid is the same in all directions ★ ARCHIMEDES’ PRINCIPLE - Pressure changes depending on the depth The magnitude of the buoyant force FB on a submerged object is equal to the weight of the fluid displaced by the Formula object. This statement is called the Archimedes Principle. Mass density Formula Pressure ★ BERNOULLI’S PRINCIPLE Hydrostatic pressure - Relates velocity, pressure, and elevation at points in aline of flow Formula L11 PASCAL, ARCHIMEDES, AND BERNOULLI’S PRINCIPLE 9 GEN PHYSICS SEM 1 | QUARTER 2 | alyssa – ♡ cramer Heat - Energy in transit from one body to another due to a difference in temperature - SI Unit of heat: Joule (J) - Another unit: Calorie (cal) - One calorie is equal to 4.186 Joules ★ THERMAL EQUILIBRIUM & ZEROTH LAW OF THERMODYNAMICS “If two systems are in thermodynamic equilibrium with a third system, the two original systems are in thermal equilibrium with each other.” ★ CONTINUITY EQUATION - Formulated in 1931 by a British physicist and astronomer Ralph H Fowler - An expression of the conservation of mass - If object A is in thermal equilibrium with object B, - The mass of the fluid passing through one section and object A is in thermal equilibrium with object of a pipe at a given time interval ∆t must pass C, then object B is in thermal equilibrium with through any section of the pipe at the same time object interval - Volumetric flow rate: product of area and velocity; has a unit of m^3/s Formula ★ TEMPERATURE SCALES Celsius scale & Fahrenheit scale Kelvin scale & Celsius scale L12 HEAT, TEMPERATURE, & THERMAL ENERGY Rankine scale & Fahrenheit scale ★ HEAT & TEMPERATURE Temperature - Defined as a measure of the average kinetic of molecules making up an object ★ THERMAL EXPANSION 10 GEN PHYSICS SEM 1 | QUARTER 2 | alyssa – ♡ cramer - Phenomenon observed in solids, liquids, and gases temperature and spontaneously flows from a - An object or body expands on the application of warmer body to a cooler body heat (temperature) - Specific Heat (c): the increase in thermal energy - Defines the tendency of an object to change its required to raise one kilogram of matter one dimension either in length, density, area, or volume Kelvin. due to heat. When the substance is heated it - Heat Transfer: is the product of specific heat, mass increases its kinetic energy and temperature change - Linear Expansion: results when an object is heated. The length changes and is directly proportional to the increase in temperature - Volume expansion: happens as linear expansion occurs - Thermodynamics: the study of the changes in thermal properties of matter - Latent heat of fusion: the amount of heat necessary to melt 1 kg of a substance to form a liquid or the amount of heat given off from a 1 kg liquid that changes to solid - Latent heat of vaporization: is the amount of heat necessary to change 1 kg of liquid to vapor or the energy is given off when 1 kg vapor condenses to produce liquid Formula Linear expansion Formula Heat Area expansion Volume expansion Linear expansion Latent heat of fusion L13 THERMAL ENERGY ★ TERMINOLOGIES - Temperature: the quantity that measures the average kinetic energy of the particle in the body - Heat: energy transferred due to a difference in 11 GEN PHYSICS SEM 1 | QUARTER 2 | alyssa – ♡ cramer Latent heat of vaporization L15 REVERSIBLE & IRREVERSIBLE PROCESSES L14 THERMODYNAMICS ★ REVERSIBLE & IRREVERSIBLE PROCESSES Reversible ★ FIRST LAW OF THERMODYNAMICS - Process whose direction can be returned to its original position by inducing infinitesimal changes Heat is a form of energy, and thermodynamic processes are, to some property of the system via its therefore, subject to the principle of conservation of energy. surroundings - Heat energy cannot be created or destroyed. - The system is in thermodynamic equilibrium with - It can, however, be transferred from one location to its surroundings another and converted to and from other forms of - It would take an infinite amount of time for the energy reversible process to finish, perfectly reversible processes are impossible Formula Irreversible processes - The system and its environment cannot return together to exactly the states that they were in - Any natural process results from the second law of thermodynamics - The sign of an irreversible process comes from the finite gradient between the states occurring in the actual process ★ HEAT ENGINE - A device that converts thermal energy to mechanical energy - Needs a high-temperature source from which heat can be removed, and a low-temperature sink wherein heat can be delivered - Ex. Automobile ★ HEAT ENGINE EFFICIENCY - A measure of how well an engine operates in L16 ENTROPY converting energy transferred by heat into work is given by the efficiency of an engine ★ ENTROPY Formula - Measure of the degree of disorder or randomness 12 GEN PHYSICS SEM 1 | QUARTER 2 | alyssa – ♡ cramer ↳ Disorder: means the particles of an object - In 1824, the French engineer Sadi Carnot analyzed moves from order to disorder state the functioning of a heat engine made a - Entropy in-universe increases fundamental discovery - When heat is added, particles in the object will be ↳ He showed that the greatest fraction of moving randomly at different speeds energy input that can be converted to ↳ Disorder follows useful work, even under ideal conditions, ↳ Gas molecules escaping from a bottle depends on the temperature difference move from a relatively orderly state to a between the hot reservoir and cold sink disorderly state ↳ Disorder increases; entropy increases - In living organisms, entropy decreases Formula ↳ But the order in life forms is maintained by increasing entropy elsewhere; life forms plus their waste products have a net increase in entropy ↳ Energy must be transformed into a living system to support life ↳ The organism soon dies and tends toward disorder - Nicholas Leonard Sadi Carnot (1796-1832), a French engineer and simply called Sadi Carnot ↳ He developed a logical proof to show that even an ideal engine would generate L18 ENTROPY CHANGE waste heat in the process of converting thermal energy into mechanical energy. ↳ Entropy, a term introduced by Clausius in - The first type of thermodynamic process is an 1865, is a measure of disorder in a system idealized process which is called the reversible process. - The second type is called the irreversible process. These processes cannot reverse themselves spontaneously and restore the system to its initial L17 SECOND LAW OF THERMODYNAMICS state - All the processes occurring in nature are irreversible ↳ There are two reasons 1. They are easy to analyze, since a ★ SECOND LAW OF THERMODYNAMICS system passes through a series of equilibrium states during a Heat will never of itself flow from a cold object to a hot reversible process object 2. They serve as idealized models to - The direction of spontaneous heat flow is from hot which actual processes can be to cold compared - Heat can be made to flow the other way, but only - To determine the change in entropy in a process that by putting in work or other energy from another is approximately reversible, the following equation source as occurs with heat pumps, air conditioners, and refrigerators, which cause heat to flow from a cooler to a warmer place - Without external effort, the direction of heat flow is from hot to cold. When work is done by a heat engine running between two temperatures, T(high) and T(low), only some of the input heat at T(high) can be converted to work, and the rest is expelled at T(low). 13