PHY 101: Mechanics - Landmark University

• PHY 101 is General Physics I (Mechanics) for Landmark University.

Course Outline

• Focus will be on space, time, units, dimensions, vectors, scalars, Differentiation of vectors, kinematics, and Newton's laws of motion.
• Includes discussion on inertial frames, impulse, force, action at a distance and conservation of momentum.
• Relative motion, application of Newtonian mechanics, and equations of motion will be covered.
• Principles in physics, like conservative forces, the conservation of linear momentum, kinetic energy, work, and potential energy, are part of the curriculum.
• Studies will cover systems of particles, center of mass, rotational motion, torque, vector product, moment, and rotation of coordinate axes and angular momentum.
• Coordinate systems, polar coordinates, conservation of angular momentum, and then on circular motion.
• Also investigates moments of inertia (gyroscopes, and precession) and Gravitation
• Newton's Law of Gravitation, Kepler's laws of planetary motion, gravitational potential energy, escape velocity, and satellite motion in orbits are all included.

Introduction

• Physics examines the relationship between matter and energy.
• Physicists look for patterns and principles in natural phenomena.
• Physical theories, laws, or principles are patterns that are well-established and widely applicable.
• Physics is an experimental science, meaning it relies on experimental observations and quantitative measurements to develop physical theories.
• Numbers are used to describe measurement results.

Space and Time

• The universe contains all space, time, matter, and energy.
• Space and time are universal, coordinating objects and existing as matter.
• Space and time are fundamental in describing the state and relationships of matter, for example motion is a relationship between position in space with time.

Concept of Space

• All physical forms have length, breadth, and height.
• Objects placed in relation to each other form systems.
• Space coordinates coexisting objects and matter states, extraposing them in quantitative relationships (alongside, above, etc).
• The term "structure of space" refers to the order in which objects and their states coexist.
• Points in space can be specified in a number of ways using Cartesian and polar coordinates.
• Cartesian coordinates fix two or three intersecting straight lines at the origin points. Reference axes are lines that intersect.
• Distances from points in space can be found by drawing parallel lines to the axes.
• Cartesian coordinates are perpendicular (rectangular) or angled (oblique).
• Positions specified using polar coordinates involve a distance (r) from the point to the origin and an angle (θ) as related to the reference axes.
• The conversion formulas between Cartesian (x,y) and polar coordinates (r, θ) are: x = r cos θ, y = r sin θ, r = √(x² + y²), θ = tan⁻¹(y/x).

Concept of Time

• Time measures the duration of events.
• Periodic events shape the perception of time, such as the rising and setting of the sun each day.
• Whether simultaneous or sequential, time helps to understand events or processes sequence and duration.
• Time coordinates states of matter.
• Structure of time refers to the order in which objects and their states occur or exist sequentially.

Units and Dimensions

• Measurement finds the size, amount, or magnitude by comparing with a standard which in turn provides a standard unit.

Physical Quantities

• Anything that can be measured (length, time, mass, temperature, and pressure).

Classification

• Fundamental (base) and derived quantities
• Scalar and vector quantities
• Dimensional and dimensionless quantities

Fundamental Quantities

• Independent of each other, those units are called fundamental units length, mass, and time are examples.
• Derived quantities are those that are derived from fundamental quantities and use derived units; velocity, acceleration, force, and work are examples.

System of units

• Complete unit sets for physical quantities.
• The CGS system uses centimeter (length), gram (mass), and second (time).
• In the FPS system, length is measured in feet, mass in pounds, and time in seconds.
• Meter for length, kilogram for mass, and second for time are the units in the MKS system.

The International System of Units

• The 14th general conference on weights and measures in 1971 established seven fundamental quantities; length, mass, time, electric current, temperature, amount of a substance, and luminous intensity.
• Length is measured in meters (m), mass in kilograms (kg), time in seconds (s), electric current in amperes (A), temperature in kelvin (K), the amount of a substance in moles (mol), and luminous intensity in candelas (cd).

Derived Units

• Velocity is measured in meters per second (m/s)
• Acceleration in meters per second squared (m/s²)
• Force/weight in Newtons (N)
• Work/heat in Joules (J)
• Pressure/stress in Pascals (P)
• Electric charge in Coulombs (C).

Metric Prefixes

• A symbol attached to the beginning of a unit of measurement denoting a fraction or a multiple of the unit, like kilo stands for multiplication of one thousand.
• Metric prefixes with negative powers; atto- (10⁻¹⁸), femto- (10⁻¹⁵), pico- (10⁻¹²), nano- (10⁻⁹), micro- (10⁻⁶), centi- (10⁻²), milli- (10⁻³)
• Metric prefixes with positive powers; kilo- (10³), mega- (10⁶), giga- (10⁹), tera- (10¹²), peta- (10¹⁵), exa- (10¹⁸).

Concept of Dimension

• The dimension of a physical quantity relates the quantity to length (L), mass (M), time (T), temperature (K or θ) and amount of substances (N).
• Area as an example has the dimension of Area = Length × Breadth, denoted as A = L × L = L².
• Velocity dimensions = Distance/Time, represented as = L/T = LT⁻¹.
• Acceleration dimensions = Velocity/Time, represented as = (LT⁻¹)/T = LT⁻².
• Force dimensions = Mass × Acceleration, represented as = M × LT⁻² = MLT⁻².
• Pressure = Force/Area dimensions: MLT⁻²/L² = ML⁻¹T⁻².
• The dimension of work = Force × Distance, represented as MLT⁻² × L = ML²T⁻².
• Power dimesions = Work/Time, represented as ML²T⁻²/T = ML²T⁻³.
• Stress dimensions = Force/Area, represented as = MLT⁻²/L² = ML⁻¹T⁻².
• Strain dimensions = Extension (Change in length) / Original Length which is dimensionless.

Applications of Dimension

• The accuracy of physical equations can be checked by applying the Homogeneity principle which states is dimensionally correct if the LHS is equal to the RHS.
• Dimensional analysis can use the above to obtain a relation between different physical quantities