Physics Study Guide: Gravitation, Rockets, Satellites, Atmospheric Pressure, and Fluid Mechanics

{"type":"doc","content":[{"type":"heading","attrs":{"textAlign":null,"level":2},"content":[{"type":"text","text":"Our Universe"}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Introduction"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This chapter explores the fundamental forces and phenomena that govern our universe, focusing on gravitation, tides, and related concepts. It provides an overview of the law of gravitation, the effects of gravity, escape velocity, tides, constellations, rockets, artificial satellites, and atmospheric phenomena such as winds, storms, and cyclones."}]},{"type":"heading","attrs":{"textAlign":null,"level":2},"content":[{"type":"text","text":"The Law of Gravitation"}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Newton's Law of Universal Gravitation"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Newton's law of gravitation states that every mass in the universe attracts every other mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers."}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Gravitational Force:"},{"type":"text","text":" The force of attraction between two bodies is given by:"}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"F = G \\frac{m_1 m_2}{r^2}"}}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"G:"},{"type":"text","text":" Universal Gravitational Constant ("},{"type":"inlineMath","attrs":{"latex":"6.67 \\times 10^{-11} \\text{Nm}^2\\text{kg}^{-2}"}},{"type":"text","text":")"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"m1, m2:"},{"type":"text","text":" Masses of the two bodies"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"r:"},{"type":"text","text":" Distance between the centers of the two bodies"}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"italic"}],"text":"Example:"},{"type":"text","text":" The gravitational force between the Earth and the Moon keeps the Moon in orbit around the Earth."}]},{"type":"heading","attrs":{"textAlign":null,"level":2},"content":[{"type":"text","text":"Gravity"}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Gravitational Acceleration and Weight"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Gravity is the force that attracts objects toward the center of the Earth. The acceleration due to gravity ("},{"type":"inlineMath","attrs":{"latex":"g"}},{"type":"text","text":") at the Earth's surface is approximately "},{"type":"inlineMath","attrs":{"latex":"9.8 \\text{m/s}^2"}},{"type":"text","text":"."}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Weight:"},{"type":"text","text":" The weight of a body is the force with which it is attracted toward the Earth."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Formula:"},{"type":"text","text":" "},{"type":"inlineMath","attrs":{"latex":"W = mg"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Variation:"},{"type":"text","text":" The value of "},{"type":"inlineMath","attrs":{"latex":"g"}},{"type":"text","text":" decreases with altitude and varies slightly with latitude."}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"italic"}],"text":"Example:"},{"type":"text","text":" A 1 kg mass has a weight of "},{"type":"inlineMath","attrs":{"latex":"9.8 \\text{N}"}},{"type":"text","text":" on Earth."}]},{"type":"heading","attrs":{"textAlign":null,"level":2},"content":[{"type":"text","text":"Escape Velocity"}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Definition and Calculation"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Escape velocity is the minimum velocity required for an object to escape the gravitational pull of a planet or celestial body without further propulsion."}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Formula:"},{"type":"text","text":" "},{"type":"inlineMath","attrs":{"latex":"v_e = \\sqrt{\\frac{2GM}{R}}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Earth's Escape Velocity:"},{"type":"text","text":" Approximately "},{"type":"inlineMath","attrs":{"latex":"11.2 \\text{km/s}"}}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"italic"}],"text":"Example:"},{"type":"text","text":" If a planet's mass and radius are double those of Earth, its escape velocity increases accordingly."}]},{"type":"heading","attrs":{"textAlign":null,"level":2},"content":[{"type":"text","text":"Tides"}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Formation and Types"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Tides are the periodic rise and fall of sea levels caused by the gravitational forces exerted by the Moon and the Sun on Earth's oceans."}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"High and Low Tides:"},{"type":"text","text":" Occur due to the relative positions of the Moon, Sun, and Earth."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Spring Tides:"},{"type":"text","text":" Occur during full and new moons when the Sun, Moon, and Earth are aligned, resulting in higher tides."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Neap Tides:"},{"type":"text","text":" Occur during the first and last quarters of the Moon when the Sun and Moon are at right angles to each other, resulting in lower tides."}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"italic"}],"text":"Example:"},{"type":"text","text":" Spring tides are stronger than neap tides due to the combined gravitational pull of the Sun and Moon."}]},{"type":"heading","attrs":{"textAlign":null,"level":2},"content":[{"type":"text","text":"Constellations and the Zodiac"}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Classification and Visibility"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Constellations are groups of stars forming recognizable patterns in the night sky. The zodiac is a band of constellations through which the Sun appears to move throughout the year."}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Table of Zodiac Constellations:"}]}]}]},{"type":"table","content":[{"type":"tableRow","content":[{"type":"tableHeader","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Sl. 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Applications"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Rockets are vehicles propelled by the expulsion of exhaust gases at high speed. Artificial satellites are man-made objects placed in orbit around Earth for communication, research, and navigation."}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Types of Rockets:"},{"type":"text","text":" Used for launching satellites and space exploration."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Artificial Satellites:"},{"type":"text","text":" Used for communication, weather forecasting, and scientific research."}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"italic"}],"text":"Example:"},{"type":"text","text":" The launch of Sputnik by Russia marked the beginning of the space age."}]},{"type":"heading","attrs":{"textAlign":null,"level":2},"content":[{"type":"text","text":"Atmospheric Phenomena"}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Winds, Storms, Cyclones, and Barometers"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Atmospheric phenomena such as winds, storms, and cyclones are driven by differences in air pressure and temperature. Barometers are instruments used to measure atmospheric pressure."}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Wind:"},{"type":"text","text":" Moving air caused by pressure differences."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Cyclone:"},{"type":"text","text":" A violent rotating wind storm."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Barometer:"},{"type":"text","text":" Measures atmospheric pressure; used to forecast weather."}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"italic"}],"text":"Example:"},{"type":"text","text":" Cyclones can cause significant destruction due to high wind speeds and heavy rainfall."}]},{"type":"heading","attrs":{"textAlign":null,"level":2},"content":[{"type":"text","text":"Floatation and Density"}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Principles of Buoyancy"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Floatation depends on the density of objects and the fluid in which they are immersed. 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It varies: maximum at the poles ("},{"type":"inlineMath","attrs":{"latex":"9.831 \\text{ m s}^{-2}"}},{"type":"text","text":"), minimum at the equator ("},{"type":"inlineMath","attrs":{"latex":"9.781 \\text{ m s}^{-2}"}},{"type":"text","text":")."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Free Fall and Escape Velocity"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Free Fall:"},{"type":"text","text":" All bodies falling freely from rest fall with equal rapidity in vacuum."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Velocity:"},{"type":"text","text":" Velocity acquired is directly proportional to time of fall."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Distance:"},{"type":"text","text":" Distance travelled is directly proportional to the square of time of fall."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Escape Velocity:"},{"type":"text","text":" Minimum velocity required to escape Earth's gravity. "},{"type":"inlineMath","attrs":{"latex":"v_{\\text{escape}} = 11.27 \\text{ km s}^{-1}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Moon's Gravity:"},{"type":"text","text":" "},{"type":"inlineMath","attrs":{"latex":"g_{\\text{moon}} = \\frac{1}{6} g_{\\text{earth}}"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":2},"content":[{"type":"text","text":"Rockets and Satellites"}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Rocket Mechanics"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Rockets operate based on Newton's third law: for every action, there is an equal and opposite reaction. The combustion of fuel produces hot gases that escape through a nozzle, propelling the rocket forward."}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Key Components:"},{"type":"text","text":" Combustion chamber, nozzle, fins, turbo-pump, propellant, liquid oxygen, instrument package, payload."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Action-Reaction Principle:"},{"type":"text","text":" The force of escaping gases (action) results in an equal and opposite force on the rocket (reaction), causing movement."}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/physics/sub_images/7c25a36e_image_1.png","alt":"Diagram of rocket parts and propulsion","title":null,"width":null,"height":null}}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Artificial Satellites"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Artificial satellites are launched into various orbits for purposes such as communication, weather forecasting, and scientific research. Multi-stage rockets are used to achieve the required speed and orbit."}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Functions:"},{"type":"text","text":" Communication, TV transmission, weather reporting, scientific exploration."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Space Probes:"},{"type":"text","text":" Used for research on other planets (e.g., Venus 13, Pioneer 10, Voyager 2)."}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"https://static.studychannel.pearsonprd.tech/study_guide_files/physics/sub_images/7c25a36e_image_2.png","alt":"Satellite orbiting Earth","title":null,"width":null,"height":null}}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Historical Space Missions"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Numerous satellites and spacecraft have been launched by various countries, contributing to our understanding of space and technology. Notable missions include Sputnik, Explorer, Vostok, Mercury, Gemini, Apollo, Skylab, Viking, Soyuz, Mir, and India's Arya Bhatta and Chandrayan-1."}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Applications:"},{"type":"text","text":" Studying stars, Earth's atmosphere, magnetic field, transmitting TV signals, space stations, planetary exploration."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Indian Achievements:"},{"type":"text","text":" Launch of Arya Bhatta, Bhaskara, Rohini, INSAT series, and Chandrayan-1."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Uses of Space Travel"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Rapid communication (telephone, TV transmission)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Exploration of outer space and heavenly bodies"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Locating water, minerals, and fish"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Navigation, air travel, weather forecasting"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Studying atmospheric radiation (X-rays, UV rays)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Production of materials and vaccines not possible on Earth"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Medical research (e.g., cancer studies)"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":2},"content":[{"type":"text","text":"Atmospheric Pressure and Barometer"}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Atmospheric Pressure"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The Earth's atmosphere exerts pressure due to the weight of air molecules. Atmospheric pressure can be demonstrated by experiments involving containers and changes in air pressure."}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Definition:"},{"type":"text","text":" Pressure exerted by atmospheric air on Earth's surface."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Measurement:"},{"type":"text","text":" Barometer is used to measure atmospheric pressure."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Torricelli's Barometer:"},{"type":"text","text":" Uses a mercury column; at sea level, height is 76 cm."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Altitude Effect:"},{"type":"text","text":" Atmospheric pressure decreases with increasing altitude."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Uses of Barometer"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Finding atmospheric pressure at a location"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"As an altimeter to determine height above sea level"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Forecasting rainfall and storms by observing pressure variations"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":2},"content":[{"type":"text","text":"Wind, Storms, and Cyclones"}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Wind Formation"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Wind is moving air, caused by differences in air pressure due to temperature variations. Air moves from high to low pressure regions, and convection currents are set up by uneven heating."}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Expansion:"},{"type":"text","text":" Air expands on heating, becomes lighter, and rises."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Convection:"},{"type":"text","text":" Warm air rises, cold air moves in, creating wind currents."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Monsoon:"},{"type":"text","text":" Seasonal winds bringing rain; direction reverses in winter."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Thunderstorms and Cyclones"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Thunderstorm:"},{"type":"text","text":" Heavy rain, lightning, thunder, wind, hail; common in hot, humid regions."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Cyclone:"},{"type":"text","text":" Violent rotating wind storm; formed by low pressure and high-speed winds."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Eye of Cyclone:"},{"type":"text","text":" Calm region at the center, surrounded by violent winds and rain."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Destruction:"},{"type":"text","text":" Cyclones can cause flooding, property damage, and loss of life."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Safety:"},{"type":"text","text":" Precautions include avoiding tall trees, metal objects, and contaminated water during storms."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Tornadoes"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Definition:"},{"type":"text","text":" Funnel-shaped cloud reaching ground; diameter 1 m to 1 km."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Speed:"},{"type":"text","text":" Violent tornadoes can reach 300 km/h."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Effect:"},{"type":"text","text":" Low pressure sucks debris and throws it out near the top."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Wind Speed and Pressure"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"High-speed wind is accompanied by reduced air pressure."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Demonstrations: Blowing over paper or between ping pong balls shows effects of pressure differences."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Anemometer: Device used to measure wind speed."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Forecasting: Satellites and radars help predict storms and cyclones."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":2},"content":[{"type":"text","text":"Floatation and Density"}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Density and Floatation"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Density determines whether a substance sinks or floats in water. Substances with density less than water float, while those with greater density sink."}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Formula:"},{"type":"text","text":" "},{"type":"inlineMath","attrs":{"latex":"\\text{Density} = \\frac{\\text{mass}}{\\text{volume}}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Density of Water:"},{"type":"text","text":" "},{"type":"inlineMath","attrs":{"latex":"1 \\text{ g cm}^{-3}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Examples:"},{"type":"text","text":" Wood, cork, oils float; iron, gold, stone sink."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Floatation:"},{"type":"text","text":" A solid immerses more in a liquid of smaller density."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Sea Water:"},{"type":"text","text":" Density varies with temperature and salinity; affects ship safety."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Ship Markings:"},{"type":"text","text":" Indicate safe submersion levels based on water density."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":2},"content":[{"type":"text","text":"Summary Table: Key Physics Concepts"}]},{"type":"table","content":[{"type":"tableRow","content":[{"type":"tableHeader","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Concept"}]}]},{"type":"tableHeader","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Definition/Formula"}]}]},{"type":"tableHeader","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Key Values"}]}]}]},{"type":"tableRow","content":[{"type":"tableCell","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Gravitational Force"}]}]},{"type":"tableCell","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"F = G \\frac{M_1 M_2}{d^2}"}}]}]},{"type":"tableCell","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"G: Universal constant"}]}]}]},{"type":"tableRow","content":[{"type":"tableCell","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Weight"}]}]},{"type":"tableCell","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"W = m \\times g"}}]}]},{"type":"tableCell","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"g = 9.8 \\text{ m s}^{-2}"}}]}]}]},{"type":"tableRow","content":[{"type":"tableCell","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Escape Velocity"}]}]},{"type":"tableCell","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Minimum velocity to escape gravity"}]}]},{"type":"tableCell","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"11.27 \\text{ km s}^{-1}"}}]}]}]},{"type":"tableRow","content":[{"type":"tableCell","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Density"}]}]},{"type":"tableCell","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\text{Density} = \\frac{\\text{mass}}{\\text{volume}}"}}]}]},{"type":"tableCell","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Water: "},{"type":"inlineMath","attrs":{"latex":"1 \\text{ g cm}^{-3}"}}]}]}]},{"type":"tableRow","content":[{"type":"tableCell","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Atmospheric Pressure"}]}]},{"type":"tableCell","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Measured by barometer"}]}]},{"type":"tableCell","attrs":{"colspan":1,"rowspan":1,"colwidth":null},"content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"76 cm Hg at sea level"}]}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"italic"}],"text":"Additional info:"},{"type":"text","text":" Academic context was added to clarify the physics principles, historical missions, and practical applications for exam preparation."}]},{"type":"paragraph","attrs":{"textAlign":null}},{"type":"heading","attrs":{"textAlign":null,"level":2},"content":[{"type":"text","text":"kepler's first law "},{"type":"text","marks":[{"type":"bold"}],"text":". The Law of Orbits"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":""}},{"type":"bold"}],"text":"Definition:"},{"type":"text","marks":[{"type":"textStyle","attrs":{"color":""}}],"text":" All planets move in elliptical orbits, with the Sun at one of the two foci."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":""}},{"type":"bold"}],"text":"Significance:"},{"type":"text","marks":[{"type":"textStyle","attrs":{"color":""}}],"text":" This disproved the long-held belief that planetary orbits were perfect circles. It introduces the concepts of perihelion (closest approach) and aphelion (farthest distance)."}]}]}]},{"type":"paragraph","attrs":{"textAlign":null}},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"The Law of Areas (Second Law)"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":""}},{"type":"bold"}],"text":"Definition:"},{"type":"text","marks":[{"type":"textStyle","attrs":{"color":""}}],"text":" A line connecting a planet to the Sun sweeps out equal areas in equal intervals of time."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":""}},{"type":"bold"}],"text":"Significance:"},{"type":"text","marks":[{"type":"textStyle","attrs":{"color":""}}],"text":" Because the orbit is an ellipse, the distance from the Sun changes. This law dictates that a planet moves faster when closer to the Sun (perihelion) and slower when farther away (aphelion)."}]}]}]},{"type":"paragraph","attrs":{"textAlign":null}},{"type":"heading","attrs":{"textAlign":null,"level":2},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"3. The Law of Periods (Third Law)"}]},{"type":"paragraph","attrs":{"textAlign":null}},{"type":"paragraph","attrs":{"textAlign":null}},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Kepler's Third Law of planetary motion establishes a fundamental relationship between the orbital period of a satellite and its distance from the central body it orbits. Specifically, this law states that the square of the orbital period (T) is directly proportional to the cube of the orbital radius (r). This relationship can be expressed mathematically as:"}]},{"type":"paragraph","attrs":{"textAlign":null}},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null}}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Significance:"},{"type":"text","text":" This provides a direct mathematical relationship between a planet's distance from the Sun and its orbital speed, confirming that planets farther from the Sun take significantly longer to complete an orbit."}]}]}]},{"type":"paragraph","attrs":{"textAlign":null}},{"type":"paragraph","attrs":{"textAlign":null}},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"image","attrs":{"src":"data:image/png;base64,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