Physics Concept Map Premedical).pdf

SYSTEM OF PARTICLES AND ROTATIONAL MOTION

CLASS XI

Centre of Mass and Centre of Gravity l

l

Rotational Motion

The centre of gravity of a body coincides with its centre of mass only if the gravitational field does not vary from one point of the body to other.

l

Mathematically,

l

Perpendicular distance of each particle remains constant from a fixed line or point and particle do not move parallel to the line. Angular displacement, q =

R

R

l

For discrete body,

For continuous body,

Centre of mass of symmetric body w

l

Equations of rotational motion w w = w0 + at w

q = w0t + at 2

w

w 2 = w02 + 2aq

R

Torque : Turning effect of the force about the axis of rotation.

Axis R1

l

Semi-circular disc,

R2

Angular momentum, Work done by torque, W = tdq Power, P = tw Axis

Motion of Centre of Mass l

For a rigid body,

w

Position,

l

w

Velocity,

Perpendicular axes theorem : Iz = Ix + Iy (Object is in x-y plane )

2R

2R

z

y

Spherical shell

Solid sphere

x

Axis A

w

l

Acceleration, If

= 0, then

(for isolated system)

CM

a

d

= constant.

If the net external torque acting on a system is zero, the angular momentum of the system remains constant, no matter what changes take place within the system. = constant; I1w1 = I2w2

Parallel axes theorem : IAB = ICM + Md 2

Axis

R b

2

B

Conservation of Angular Momentum l

Axis

Moment of Inertia

For a system of particles

w

L

R

L

L

l

l

Axis

Axis

Semi-circular ring, l

w

Axis

Angular acceleration, a = l

w

Axis

I = MR2

Angular velocity, w = w

Axis

Rolling Motion

Equilibrium of a Rigid Body l

l

A rigid body is said to be in mechanical equilibrium, if both of its linear momentum and angular momentum are not changing with time, i.e., total force and total torque are zero. Linear momentum does not change implies the condition for the translational equilibrium of the body and angular momentum does not change implies the condition for the rotational equilibrium of the body.

I = MR /2

l

For a body rolling without slipping, velocity of centre of mass vCM = Rw Kinetic energy, K = Ktranslational + Krotational =

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MECHANICAL PROPERTIES OF SOLIDS AND FLUIDS CLASS XI RELATION BETWEEN Y, B, G AND s l Y = 3B(1 –2s) l Y = 2G(1 +s)

Young’s modulus Bulk modulus,

APPLICATION OF ELASTICITY Designing beams for bridges The depression in rectangular

l

l

beam,

Compressibility, k = 1/B

l

ELASTIC POTENTIAL ENERGY HOOKE’S LAW

Modulus of rigidity

Stress µ Strain or Stress = E ´ Strain, (E = modulus of elasticity)

P.E. stored per unit volume of stretched wire,

Poisson’s ratio s

ELASTICITY AND PLASTICITY STRESS AND STRAIN l

l

VISCOSITY Coefficient of viscosity: where

is the velocity

gradient between two layers of liquid.

BERNOULLI’S THEOREM Bernoulli’s theorem : For the streamline flow of an ideal liquid, the total energy per unit volume remains constant

Stoke’s law : Backward dragging force on a spherical body, F = 6 phrv.

Basic results on viscosity

PROPERTIES OF SOLIDS PROPERTIES OF FLUIDS FLUIDS IN MOTION

FLUIDS AT REST

PRESSURE Pascal’s law The pressure is same at all points inside the liquid lying at the same depth in a horizontal plane. Gauge pressure = P – P0 = hrg. ARCHIMEDE’S PRINCIPLE

Reynold’s number : Determines

When a body is immersed fully or partly in a liquid at rest, it loses some of its weight, which is equal to the weight of the liquid displaced by the immersed part of the body.

nature of fluid flow

Apparent weight

Poiseuille’s formula

(For fully immersed body)

Elasticity : Ability of a body to regain its original shape, on removing deforming force. Plasticity : The inability of a body to regain its original size and shape on the removal of the deforming forces.

SURFACE TENSION Surface tension: The property by which the free surface of liquid at rest tends to have minimum surface area. Surface energy: Work done against the force of surface tension in forming the liquid surface.

CAPILLARITY The phenomenon of rise or fall of liquid in a capillary tube is called capillarity. Height of the liquid within capillary tube Where, q = angle of contact r = density of liquid a = radius of tube

In an air bubble

Excess Pressure

Inside a soap bubble

Inside a liquid drop

0

1

273

SHM IN SPRING

FORCE LAW IN SHM

GENERAL EQUATIONS OF SHM

DAMPED AND FORCED OSCILLATIONS

SIMPLE PENDULUM

ENERGY IN SHM

ELECTRIC FLUX

ELECTROMAGNETIC INDUCTION

CLASS XII

Combination of Inductors

Magnetic Energy l

l

Energy stored in an inductor,

l

Inductors in series,

l

Inductors in parallel,

l

If coils are far away, then M = 0.

Energy stored in the solenoid,

L–R Circuit l Current growth in L–R circuit l

So,

Current decay in L–R circuit, Here,

l

Magnetic energy density,

Inductance

Lenz's Law l

l

l

The direction of the induced current is such that it opposes the change that has produced it. If a current is induced by an increasing(decreasing) flux, it will weaken (strengthen) the original flux. It is a consequence of the law of conservation of energy.

l

Emf induced in the coil/conductor,

l

Coefficient of self induction,

l

Self inductance of a long solenoid,

l

Mutual inductance,

l

Mutual inductance of two long coaxial solenoids,

l

Induced Electric Field l

It is produced by change in magnetic field in a region. This is non-conservative in nature.

l

This is also known as integral form of Faraday’s law.

Coefficient of coupling, For perfect coupling, k = 1 so,

Magnetic Flux and Faraday's Law l l

Energy Consideration in Motional emf l

Emf in the wire, e = Bvl

l

Induced current,

l

Force exerted on the wire,

Magnetic flux Faraday’s law : Whenever magnetic flux linked with a coil changes, an emf is induced in the coil. w

Induced emf,

w

Induced current,

w

Induced charge flow ,

Electric Generator l

I l

B ×

v

F

R l

Motional emf

Power required to move the l

wire, It is dissipated as Joule’s heat.

l

On a straight conducting wire, e = Bvl On a rotating conducting wire about one end, Here,

are perpendicular to each other.

l

l

Mechanical energ y is converted into electrical energy by virtue of electromagnetic induction. Induced emf, e = NABw sinwt = e0sinwt Induced current,

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RAY OPTICS AND OPTICAL INSTRUMENTS CLASS XII w w w w

APPLICATIONS OF TIR Fiber optics communication Medical endoscopy Periscope (Using prism) Sparkling of diamond

t ligh ible Vis

P Deviation of red light(dR) A (i– r1) (e– r 2) Deviation of d N2 N1 R violet light (dV) e i O r r q 1 2 F G Y G E N B H Angular I spread V Q R Screen

REFRACTION THROUGH PRISM TOTAL INTERNAL REFLECTION TIR conditions w Light must travel from denser to rarer. w Incident angle i > critical angle ic Relation between m and ic:

Relation between m and dm where, dm = angle of minimum deviation A = angle of prism

Snell’s law: When light travels from medium a

Power of lens :

f Combination of lenses: Power: P = P1 + P2 – dP1P2 (d = small separation between the lenses) For d = 0 (lenses in contact) Power: P = P1 + P2 + P3 + ...

THIN SPHERICAL LENS Thin lens formula :

or d = m – 1 A (Prism of small angle) Angular dispersion

f

Magnification:

= dV – dR = mV – mR A

REFRACTION OF LIGHT

POWER OF LENSES

Dispersive power,

REFRACTION BY SPHERICAL SURFACE

to medium b, Refractive index,

Mean deviation,

Relation between object distance (u), image distance (v) and refractive index (m) (Holds for any curved spherical surface.)

Real and apparent depth Lens maker’s formula f

REFLECTION OF LIGHT According to the laws of reflection, Ði = Ðr If a plane mirror is rotated by an angle q, the reflected rays rotates by an angle 2q.

SIMPLE MICROSCOPE Magnifying power For final image is formed at D

RAY OPTICS

Mirror formula,

OPTICAL INSTRUMENTS

(least distance)

REFLECTING TELESCOPE Magnifying power f f f

f

Magnification, m =

COMPOUND MICROSCOPE Magnifying power, M = mo × me For final image formed at D (least distance)

f For final image formed at infinity f

REFLECTION BY SPHERICAL MIRRORS

f

f

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TELESCOPE

f

Astronomical telescope For final image formed at D (least f f distance) f In normal adjustment, image formed at infinity M = fo / fe

f

TERRESTRIAL TELESCOPE f For normal adjustment f Distance between objective and eyepiece d = fo + 4f + fe

Electron orbits and their energy

A. Fission

B. Fusion

EXTRINSIC SEMICONDUCTORS

JUNCTION TRANSISTOR

INTRINSIC SEMICONDUCTORS

SEMICONDUCTOR DIODE

BIASING CHARACTERSTICS APPLICATIONS OF DIODE APPLICATIONS OF TRANSISTOR

CE(n-p-n)

Amplifier