General classifications:

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1 General classifications: Physics is perceived as fundamental basis for study of the universe Chemistry is perceived as fundamental basis for study of life Physics consists of concepts, principles and notions, based on Mathematics. Physics Optics Thermophysics Electrophysics Mechanics Atomic Physics Nuclear Physics Astrophysics Geophysics Biophysics study of light study of heat study of electricity study of motion study of atoms study of nuclei celestial study study of earth study of Biological systems Definition of Mechanics: Physics of motion and movement. Mechanics: Classical Quantum Classical Mechanics macro-world, position, velocity, etc. Quantum Mechanics micro-world, atomic level, sub-atomic level

2 Classical Mechanics o Classical Mechanics assumes continuous flow. o Classical Mechanics describes objects by position and momentum. o Classical Mechanics is the Newtonian Mechanics. Classical Mechanics Statics Kinematics Dynamics (Kinetics) Statics deals with objects at rest or in equilibrium. Kinematics describes Geometry of motion. Kinematics deals with displacement, position, velocity, acceleration, and so on Dynamics is a study of relation between forces and motion. Dynamics describes the cause. Definitions and equations in Physics and Mathematics. macroscopic objects astronomical objects visible entities in large-scale celestial bodies in universe point object system structureless, no dimension (no diameter), orientation does not matter has dimension group of objects

3 Degrees of Freedom is an independent physical parameter, which formally describes the state of a physical system is directions in which independent motion can occur is total number of independent displacements of motion pseudovector versus polar vector pseudovector = axial vector pseudovector under an improper rotation (reflection) in 3-dimension, gains additional sign flip equal magnitude, opposite direction Geometrically, not mirror image pseudovector not mirror image

4 polar vector = real vector polar vector in 2-dimension has magnitude and direction in 2-dimension can also have length and angle on reflection, matches with its mirror image acceleration = a vector quantity, which is the rate of change of velocity with respect to time a v t final final v t initial initial v t Average acceleration = a av dv dt constant velocity = zero acceleration Force = a push or pull upon an object changing its motion angular velocity = rotational velocity angular motion angular velocity = the rate of change of angular displacement of a rotating body.

5 r = radius s = arc length θ = angular displacement s r Peripheral length = 2 r

6 angular velocity t = time r = radius = angular velocity f = angular frequency v t = tangential velocity = angular displacement final initial vt 2f t t t t final initial d average dt angular acceleration = the rate of change of angular velocity with respect to time t t angular acceleration = 2 In angular rotation, inertia takes place of mass.

7 moment of inertia = the resistance to change in rotational motion moment of inertia I = mass X (diatance from axis) 2 = m X r 2 torque = the rate of change of angular momentum torque = moment of inertia X angular acceleration = I. torque = the angular force that is causing rotation. = r F sin θ momentum = the property of motion of moving objects due to their mass. linear momentum p = m.v angular momentum L = I. m = mass of the object v = linear velocity of the object I = moment of inertia = angular velocity of the object angular momentum L = linear momentum distance from the axis = p. r = m.v.r m = mass of the object v = linear velocity of the object r = distance from the axis work = an activity involving a force and movement in the direction of the force.

8 Potential Energy Kinetic Energy stored energy, resulting from object s position results from object s motion, converted from potential energy E potential M = mass of the earth m = mass of the object v = velocity of the object GMm r r = distance from the center of the earth Ekinetic 1 mv 2 2 Work-Energy Principle = the change in the kinetic energy of an object = the net work done on the object power = work time ( force) ( dis tan ce) time dis tan ce ( force) time ( force) ( velocity)

9 Newton s Law of Gravity 1) Any two objects exert a gravitational force of attraction on each other 2) The direction of the force is along the straight line joining the objects 3) The magnitude of the force (mass of object 1) X (mass of object 2) 4) The magnitude of the force (the distance between them) 2 m m F1 G F 2 2 G 2 r G = Newton s constant m m r mass versus weight mass = how much material the object contains weight = measure of the gravitational force exerted on that material gravitational force mass

10 Newton s Laws of Motion Newton s 1 st law of motion inertia Newton s 2 nd law of motion more mass, greater force Newton s 3 rd law of motion action reaction Newton s 1 st law of motion: without applied force, objects at rest will remain at rest. without applied force, moving objects will continue constant velocity. Newton s 2 nd law of motion: Force = mass X acceleration magnitude of acceleration applied force magnitude of acceleration (mass of the object) 1 Newton's 3 rd law of motion: For every action, there is an equal and opposite reaction. In every interaction, there is a pair of forces acting on the two interacting objects. Quantum Mechanics Study of Photoelectric Effect led to an improved understanding of Quantum Mechanics. Photoelectric Effect = light hits a material and ejects a single electron. Photoelectric Effect tells us energy consists of discrete quanta instead of a continuum. Quantum Theory explains the nature and behaviour of matter and energy in the atomic/sub-atomic world.

11 Quantum Theory states that, Electrons can only absorb/emit energy in discrete packets (quanta). Energy of each quanta is proportional to the frequency of radiation. Development of Quantum Theory: Max Planck (1900) Albert Einstein (1905) Louis de Broglie (1924) Werner Heisenberg (1927) quantization of energy quantization of radiation Wave-Particle Duality Uncertainty Principle Proposed quantization Beam of light is stream of particles. Electro-magnetic radiation exists in multiple packets. Quantized form of electro-magnetic energy E E = h ħ = h/2 E = ħ E = energy of the photon = frequency of the radiation h = Planck s constant = angular frequency turning point of Quantum Mechanics Black-Body Radiation (1859) Max Planck s solution (1900) Photoelectric effect (1887) Einstein s explanation (1905)

12 the key difference between Quantum and Classical Mechanics is the role of probability Classical Mechanics presupposes that, exact simultaneous values can be assigned to all physical quantities, whereas, Quantum Mechanics denies this possibility. According to Quantum Mechanics, when an object s position is established precisely, the object s momentum becomes more uncertain. Einstein s Theory of Special Relativity This theory concerns: stationary observer light speed in vacuum space-time concept 1) The laws of Physics are the same for all non-accelerating observers, observer at rest as well as observer at constant speed. 2) The speed of light within a vacuum is the same, irrespective of observer s motion. 3) Space and time are combined into a complex intricate concept of a single continuum known as space-time. Concept of Space-Time Curvature (1915) Massive objects cause a distortion in space-time, which is felt as gravity. Space-Time distortion is governed by the Lorentz Transformations. event = something happening at a certain point in space-time.

13 Frame of Reference Inertial Non-Inertial relative motion with constant velocity accelerating in curved paths Space and time distort when the inertial reference frame approaches the speed of light. An event in any inertial frame is specified by Cartesian coordinates x, y, z, along with time coordinate t. Frame of Reference F1 Frame of Reference F2 x 1, y 1, z 1, t 1 x 2, y 2, z 2, t 2 1) Lorentz Transformation are coordinate transformations between 2 coordinate frames moving at constant velocity relative to each other. 2) Hendrik Lorentz (1895) explained how speed of light is the same in all inertial reference frames. Such invariance of light speed is one of the postulates of Special Relativity.

14 3) Lorentz Transformation refers to transformations between inertial frames in the context of Special Relativity. According to Einstein s 2 nd postulate of relativity Expressing mathematical consequence of invariance of speed of light The Lorentz transformation is in accordance with Special Relativity, but was derived BEFORE Special Relativity. The space-time curvature is directly determined by distribution of matter and energy. space-time curvature distribution of matter & energy equivalence of mass & energy

15 Mass-Energy Equivalence 1) is a consequence of Special Relativity. 2) is derivations of the Lorentz transformation. 3) describes the foundations of Special Relativity. 4) arose originally from Special Relativity. Mass-Energy Equivalence is a concept formulated by Albert Einstein. Mass-Energy Equivalence explains the relationship between mass & energy. It is expressed as, E = mc 2 E = energy content of a physical system at rest m = mass of the system c = speed of light in a vacuum (310 8 m/s) Einstein proposed that, 1) mass-energy equivalence is a general principle, 2) and it s a consequence of the symmetries of space & time.

16 Einstein s Theory of General Relativity Einstein s Theory of General Relativity is the geometric theory of gravitation published in Classical Mechanics demonstrates the action of the force of gravity (free-fall, orbital motion). On the other hand, General Relativity corresponds to inertial motion within a curved Geometry of space-time. Einstein s Theory of General Relativity generalizes Theory of Special Relativity and Newton s Law of Universal Gravitation. Einstein s Theory of General Relativity provides a unified description that, the curvature of space-time is directly related to the energy and momentum of matter and radiation. Heisenberg Uncertainty Principle Complementary Variables = Conjugate Pairs = specific pairs of physical properties of a particle. Examples: position & momentum, energy & time.

17 This principle asserts fundamental limit to the precision of the measurement of position & momentum. Simultaneous precise measurement of conjugate (complementary) pairs is not possible at a given moment. The mathematical form of the uncertainty principle relates complementary to Planck's constant. Δ = uncertainty in the variables h = Planck s constant The Schrödinger Theory This principle provides a formal method of treating the dynamics of physical particles in terms of associated waves. Erwin Schrödinger s postulate The discrete frequencies in the atomic spectra: are not due to discontinuous transitions (quanta), but it s due to a resonance phenomenon.

18 units speed velocity m/s or ft/s acceleration m/s 2 moment of inertia kg.m 2 or ib.ft 2 momentum kg.m/s torque Newton.metre force Newton pressure Pascal, Newton/m 2 work energy Joule, Newton/m power Watt, Joule/s