Physics Time and Vectors Quiz

General Physics 1 (Mechanics)

• Course taught by Prof. M.E. Emetere
• Part 1 of the course
• Topics include space and time, units and dimensions, vectors and scalars, differentiation of vectors, and kinematics.

Table of Contents

• Space and time
• Units and dimensions
• Vectors and scalars
• Differentiation of vectors
• Kinematics

Space and Time

• Native understanding of space and time often taken for granted.
• Space considered as emptiness, time as ticking incessantly.
• Space and time have complex concepts in physics.
• Unifying physics theories is challenging due to the complexities of space and time.
• E = ma, E = mc², dS > 0, 8πG, G + ΔG = 8πGT
• Specific topics like Absolute Time and Relatively Time will be discussed.

Introduction

• Native understanding of space and time is straightforward.
• Physicists struggle with space and time from a more complicated perspective, as the concept makes physics theories challenging.
• Diverse interpretations exist across branches of physics.
• Learning objectives for the lecture include identifying types of space and time, delving into the classical and relativistic views of space and time, understanding the differences between these perspectives and quantum mechanics, and solving classical view problems of space and time.

Types of Time

• Absolute time
• Relative time
• Proper time
• Coordinate time
• Psychological time
• Biological time
• Universal time
• Atomic time
• Sidereal time
• Solar time
• Planck time
• Historical time
• Cosmological time
• Clock time
• Dynamical time
• Event Time

Absolute Time

• Time flows uniformly, regardless of external factors (Newtonian physics).
• Time is the same for all observers, independent of their motion or position.
• Example: A clock ticks at the same rate regardless of location or movement.

Relative Time

• Time is not absolute but relative (Einsteinian relativity).
• Time depends on the observer's speed and position in a gravitational field .
• Time can slow down or speed up relative to the difference between observers.
• Example: Time slows down for astronauts moving at high speeds compared to those on Earth due to time dilation, or time can pass more slowly for objects in a stronger gravitational field.

Proper Time

(Relativity)

• Time interval measured by an observer moving along a specific trajectory.
• the time an object/observer experiences in his/her own frame of reference.
• Example: An astronaut in space experiences proper time which could be different from someone on Earth.

Coordinate Time

• Time measured by an observer using a fixed reference frame.
• Used to describe events occurring at different spatial locations.
• Example: The International Celestial Reference System (ICRS) is an example of coordinate time.

Psychological Time

• Subjective experience of time.
• Varies depending on circumstances, emotions, and mental states.
• Example: Time feels faster during enjoyable activities and slower when bored or anxious.

Biological Time

• Natural cycles that govern living organisms (e.g., circadian rhythms).
• Internal clock that regulates physiological processes in animals and plants.
• Example: The human sleep-wake cycle follows a 24-hour pattern.

Universal Time

• Time standard based on Earth's rotation.
• Essentially the same as Greenwich Mean Time (GMT).
• Used in astronomy, navigation, and broadcasting for reference.
• Example: UT (Universal Time) is used in global communications and positioning systems.

Atomic Time

• Measured using vibrations of atoms (e.g., cesium atoms) that oscillate at very precise frequencies.
• International System of Units (SI) defines a second based on atomic time.
• Example: International Atomic Time (TAI) is a time standard crucial for extremely accurate timekeeping, used in GPS systems.

Sidereal Time

• Timekeeping system used by astronomers.
• Tracks Earth's rotation relative to distant stars (rather than the Sun).
• Shorter than a solar day.
• Example: Used in celestial navigation and for aligning telescopes.

Solar Time

• Based on the position of the Sun.
• Measures time according to Earth's rotation relative to the Sun.
• Apparent solar time refers to the precise Sun's position.
• Mean solar time is the average.
• Example: Sundials measure apparent solar time. Modern clocks are based on mean solar time.

Planck Time

• Smallest meaningful unit of time in quantum mechanics.
• Shortest time for light to travel one Planck length (the smallest measurable distance in the universe) in a vacuum.
• On the order of 10-43 seconds.
• Example: Important in theoretical physics, especially in discussing the Big Bang and quantum gravity.

Historical Time

• Understanding time in terms of human history.
• Divided into eras, epochs, centuries.
• Example: Geological Time Scale and the Anthropocene Epoch.

Cosmological Time

• Refers to time on the largest scales of the universe from the Big Bang to the present.
• Used to measure the age and evolution of the universe.
• Example: The universe is about 13.8 billion years old according to cosmological time.

Clock Time

• Everyday, practical time measured by clocks.
• Divided into hours, minutes, and seconds.
• Example: Standard 24-hour clock systems.

Dynamical Time

• Used in precise measurement of planetary motion.
• Example: Astronomers use dynamical time to predict celestial body positions (like planets).

Event Time

• Duration of an event.
• Varies from one geographical region to another.
• Depends on the chosen time system.
• Example: Unlike a standard 24-hour system; it's crucial for coordinating events, whose timing is location dependent.

Types of Space

• Physical space (and its real-world counterparts).
• Euclidean space (geometry applied).
• Non-Euclidean space (no Euclidean geometry).
• Curved space, including Riemannian space.
• Minkowski space
• Metric space
• Topological space
• Hilbert space
• Phase space
• Personal construct space

Physical Space

• Three-dimensional continuum where objects exist and events occur.
• Example: Our everyday experience of surroundings including rooms, the atmosphere or outer space.

Euclidean Space

• Space governed by the rules of Euclidean geometry.
• Parallel lines never intersect, angles in a triangle sum to 180°

Non-euclidean Space

• Where Euclidean geometry doesn't apply due to space curvature.
• Includes spherical (curved surfaces like Earth) or hyperbolic geometries.

Curved Space (Riemannian Space)

• Space is curved by the presence of mass and energy.
• Not flat; gravitational fields warp spacetime.
• Example: Light bending around stars resulting from gravitational lensing predicted by general relativity.

Minkowski Space

• Four-dimensional framework (spacetime) in special relativity.
• Includes time as a dimension alongside spatial dimensions.

Vector Space

• Mathematical structure used for adding vectors and scaling them by numbers (scalars), fundamental in linear algebra.
• Vectors (displacement, velocity, force) are represented in 3D space.

Outer Space

• Vast expanse beyond Earth's atmosphere (space/cosmos).
• Stars, planets, and galaxies reside here..
• Example: The regions where astronauts travel during space missions go far beyond Earth's gravitational influence.

Classical View of Space and Time

• Space and time considered absolute and separate by Isaac Newton.
• Space a fixed, unchanging stage for objects' motion with a fixed frame of reference.
• Time flows uniformly—different from observer motion.
• Example: Newton's concept of time is uniform for everyone, independent of their movement and position.

Relativity View of Space and Time

• Einstein's relativity overthrew traditional understanding of space and time.
• Time and Space aren't independent but an interwoven entity (spacetime).
• Different observers have different perceptions of space and time.
• Spacetime curves in the presence of mass and energy, the root of gravity.
• Example: Gravitational lensing results from the bending of spacetime by massive objects like stars and planets

Relativity View of Space and Time (Special relativity)

• Space and time are relative to the observer's motion.
• Events that seem simultaneous from one observer's perspective can be divided in time by a different observer.
• Time dilates (slows down) at high speeds.
• Length of an object shrinks to be shorter if it is moving with respect to the observer in the direction of motion.
• Example: Time slows down for astronauts compared to people on Earth (time dilation).

Kinematics

• Study of motion without considering the forces.
• Describes an object's motion in terms of kinematic quantities.
• Kinematic quantities (distance, displacement, speed, velocity, acceleration) are used to describe the motion of an object.

Formulae for Constant Acceleration

• Five equations, useful for calculating missing quantities in uniformly accelerated rectilinear motion.
• These concepts are useful for describing continuous motion.
• Example equations: v = u + at, s = ut + ½at² and v² = u² + 2as.

Test your knowledge of time concepts and vector notation in physics. This quiz covers various types of time, the SI unit system, and how to express vectors in component notation. Perfect for students looking to solidify their understanding of these fundamental topics.