Category: Physics Notes PPT

Albedo is a calculation of diffuse solar radiation reflected from the total solar radiation, and it’s determined on a range of zero to 1, with 0 corresponding to a black body that absorbs every incident radiation and 1 corresponding to a body that reflects almost every incident radiation.

The ratio of radiosity to irradiance (flux each unit of area) obtained by a surface is known as surface albedo. The proportion reflected is defined by the spectral and angular spread of solar radiation approaching the surface of the Earth, as well as the characteristics of the surface itself. These variables change with the composition of the atmosphere, geographical region, and time.

Albedo Effect Definition: Albedo effect has been the directional integration of reflectance across all solar angles in a particular time, whereas bi-hemispheric reflectance is measured for a specific angle of incidence (that is, for a particular location of the Sun). The temporal resolution can vary between seconds to regular, weekly, or yearly averages (as determined by flux measurements).

The albedo effect involves a wide range of spectrum of solar radiation unless it is provided for a particular wavelength (spectral albedo). It is frequently provided for the range wherein the majority of solar energy enters the surface (between 0.3 and 3m) due to measurement constraints. 

Such spectrum includes visible light (0.4–0.7 m), that describes why surface albedo with such a low albedo (– for example, trees) look dark and surfaces with a large albedo look bright (e.g., snow reflects major radiation).

Albedo is a key concept in astronomy, climatology, and sustainable development (for example, in the Leadership in Energy and Environmental Design (LEED) programme for building sustainability rating). Because of cloud cover, the Earth’s average albedo from the upper atmosphere, or planetary albedo, is 30–35 percent, although it varies greatly locally from across the surface due to various geological and environmental properties.

Johann Heinrich Lambert’s work Photometria, published in 1760, was the first to use the word albedo in optics.

Terrestrial Albedo Meaning

In visible light, albedo ranges from around 0.9 for new snow to almost 0.04 for charcoal, including some of the darkest materials. Deeply shadowed cavities will reach the black body’s active albedo of zero.

The ocean surface, like most trees, does have a low albedo when viewed from afar, while desert areas were some of the highest albedos across landforms. The majority of land areas have an albedo of 0.1 to 0.4. Earth’s average albedo has been about 0.3. Due to the contribution of clouds, it’s much greater than for the seas. NASA’s MODIS instruments on deck the Terra and Aqua satellites, as well as the CERES instrument on the Suomi NPP and JPSS, are used to measure the Earth’s surface albedo on a regular basis. Since satellites could only calculate the amount of reflected radiation in one direction, rather than all directions, a mathematical model is being used to convert a sample collection of satellite reflectance measurements into predictions of bi-hemispheric reflectance and directional-hemispherical reflectance.

The bidirectional reflectance distribution function (BRDF), that explains how well the reflectance of a given surface varies depending on the observer’s view angle and the solar angle, is used in such calculations. BDRF may aid in the conversion of reflectance observations into albedo.

Examples of Terrestrial Albedo Effects

1. Illumination:

Apart from situations in which a variation in illumination causes a change in the Earth’s surface at that spot, albedo is indeed not dependent solely on illumination as increasing the amount of incident light proportionally affects the quantity of reflected light (for example, through melting of reflective ice).

2. Insolation Effects:

The degree of albedo temperature effects is determined by the quantity of albedo as well as the extent of local insolation (solar irradiance); high albedo areas in the arctic and antarctic regions seems cold because of low insolation, while high albedo areas in the Sahara Desert, that also have a significantly higher albedo, would be warmer due to increased insolation.

3. Albedo–Temperature Feedback:

A snow–temperature input occurs when the albedo of a region changes due to snowfall. A film of snowfall raises local albedo, which reflects sunlight and cools the region. In theory, if no outdoor temperature changes, the increased albedo and lower temperature will maintain the entire snow and invite more snowfall, deepening the snow–temperature response.

4. Snow:

Snow albedo varies dramatically, varying from 0.9 for freshly fallen snow to 0.4 for snow melt and even as low as 0.2 for dirty snow. Ice albedo in Antarctica measures somewhat more than 0.8. As a marginally snow-covered region warms, the snow melts, reducing the albedo and thereby causing more snowmelt as the snowpack absorbs additional radiation.

5. Solar Photovoltaic Effects:

The electrical energy production of solar photovoltaic systems may be affected by albedo. Distinctions in the spectrally weighted albedo of solar photovoltaic techniques are dependent on hydrogenated amorphous silicon (a-Si:H) and crystalline silicon (c-Si) compared to the standard spectral-integrated albedo predictions, for instance, show the effects of a spectrally sensitive albedo. According to research, the effects can be as high as 10%. The study was recently expanded to include the consequences of spectral bias due to specular reflectivity of 22 frequently occurring surface materials, as well as the effects of albedo on the output of seven photovoltaic materials, including three common photovoltaic system topologies: commercial flat rooftops, industrial, and residential pitched-roof installations.

Astronomical Albedo

Satellites, Planets, and minor planets like asteroids have albedos that can be used to conclude a lot regarding their properties. A significant portion of the astronomical field of photometry is the research of albedos, whose reliance on lighting angle, wavelength, and time variation. Most of what we understand about small and distant objects which cannot be clarified by telescopes arises from studying the albedos. The absolute albedo, for instance, will reveal the surface ice composition of bodies in the outer Solar System, while the variation of albedo through phase angle reveals regolith properties, and exceptionally high radar albedo indicates the high metal concentrations in asteroids.

With an albedo of 0.99, Enceladus, a moon of Saturn, does have one of the highest recorded albedos of just about anybody throughout the Solar System. The albedos of several tiny items in the outer Solar System and asteroid belt are as small as 0.05. The albedo of a standard comet nucleus is 0.04. A basic and intensely space weathered layer containing certain organic compounds is assumed to be the source of this kind of dark surface.

The Moon’s overall albedo is estimated to be about 0.14, but it is highly directional and non-Lambertian, with a serious opposition impact. Even though reflectance characteristics of regolith surfaces on airless Solar Syste
m bodies vary from that of the terrestrial terrains, these are common.

In Physics, we define angular acceleration as the time rate of change of angular velocity. This angular acceleration definition is plain because there are two types of angular velocity, spin angular velocity, and orbital angular velocity. This leads to two kinds of angular acceleration as well; spin angular acceleration and orbital angular acceleration. 

Angular motion occurs when an object is moving in a rotational manner. The object’s velocity is always changing while it is moving in a circular path.

A good example to understand angular acceleration is a disk with an axle in its center.

The disk rotates about its center. However, at the edge of the disk, an arrow is bolted. This arrow cannot change its orientation relative to the disk. The disk is then rotated.

The speed of the spinning disk is always changing. Therefore, the disk is said to have angular acceleration, since its velocity is constantly changing with time.

Velocity is a vector quantity that involves speed with velocity. When in a circular motion, the direction of every point on the object is changing constantly.

The unit of angular velocity can be expressed as radian/second. It explains the speed at which the object rotates and provides the direction of a rotating object.

There are two versions of angular acceleration, average angular acceleration and instantaneous angular acceleration. Average angular acceleration is an average calculation involving multiple values divided by the total number of values being considered.

The angular acceleration at a very specific moment of time is called instantaneous angular acceleration.

Types of Angular Acceleration

Spin angular acceleration is said to relate with the angular acceleration of the rigid body to its center of rotation, and orbital angular acceleration is defined as the angular acceleration of a point particle about a fixed origin. Angular acceleration is measured in units of angle per unit time squared (as per SI unit – radians per seconds squared) and represented by the ‘α’ symbol.

The angular acceleration formula is given by

α= ∆ω/∆t

where ∆ω is a change in angular velocity and ∆t is the time interval.

When uniform rotation is considered, both the average and instantaneous values opt to coincide. We will provide angular acceleration examples below – 

Orbital Angular Acceleration of a Point Particle: Two-Dimensions

Orbital angular acceleration can be defined as the rate at which the two-dimensional orbital angular velocity of the particle changes from the origin. The instantaneous angular velocity ω at any point in the time is given by 

ω=v˔/r

Where r is the distance from the origin and v˔ is the cross-radial component of the instantaneous velocity, which, by convention, is positive for counterclockwise motion and negative for a clockwise motion.

Therefore, the instantaneous angular acceleration α of the particle can be given by 

α = d/dt (v˔/r)

expanding the right-hand side using the product rule from different calculus

α = 1/r d v˔/dt – v˔/r² dr/DT

In the special case where the particle undergoes circular motion about the origin, d v˔/dt becomes tangential acceleration a˔, and dr/dt goes out since the distance from the origin remains constant, 

so the equation gets simplified as α = a˔/r

In two dimensions, angular acceleration is a number with a plus or minus sign indicating orientation but not pointing in a direction. If the angular speed increases counterclockwise or decreases clockwise, the sign is taken as positive. If the angular speed increases clockwise and decreases counterclockwise, then the sign is taken as negative.

Relation between Angular Acceleration and Linear Acceleration.

At = Δv/ Δt

However, in a circular motion, linear velocity v is a product of radius of curvature (r) and Angular velocity ω.

v = rω

Therefore linear acceleration At is given as,

A[_{t}] = Δ(rω)/ Δt

Now, The radius r is constant for circular motion. 

So,

Δ(rω) = r(Δω). 

Therefore,

A[_{t}] = rΔω/ Δt    ….(i)

By definition, angular acceleration is given as

α = Δω/Δt

Therefore, the equation (i) changes to

A[_{t}] = rα

Or 

α= [frac{A_{t}}{r}]

Therefore, it can be proved that linear acceleration and angular acceleration are directly proportional.

Application of Angular Acceleration

The concept of angular acceleration is seen in a merry go round in a park. When a child sits on the horse and starts the merry go round from rest, there is an angular acceleration ω which constantly changes. The object, which is the merry go round, is spinning and its speed is also changing. Therefore, it can be said that the object is accelerating angularly.

The faster the machine moves, the greater is the angular acceleration. Care should be taken while designing the merry go round that the angular acceleration doesn’t exceed its limits and the rise is safe for children.

Angular acceleration can also be seen in a giant wheel. Once it starts operating it has to speed up and slow down. This gives it the angular velocity. If it speeds up at a constant rate then we can say that the angular acceleration is constant. Rarely does a giant wheel speed up at a constant rate. Hence we can say that the angular acceleration in a giant wheel is constantly changing. 

Have you ever wondered why helicopter blades are so long and far away from the center point? Let’s explore why. The center point is called the pivot. This is the point from where the force is applied to move the blades in rotational motion. Now, the farther the force is applied from the pivot, the greater is the angular acceleration.

 

When the angular acceleration is greater, it then becomes easier for the helicopter to lift itself up in the air and fly at a safe distance above the earth, fighting the gravitational pull exerted by the earth.

This is the reason behind having large blades in helicopters. To provide greater angular acceleration and fly easily.

Test Angular Acceleration

There are two experiments illustrated here for students to understand angular acceleration.

Experiment 1:

Take a wire or a thin rope. Now hold near one of its ends and try rotating it. The wire or rope will not rotate freely and you will face difficulty in rotating it. Therefore, there will be little to no angular acceleration in this type of motion.

Experiment 2:

Take the same wire or rope. Now, instead of holding it near its end, hold it in the middle or closer to the other end. And rotate it. You will observe that the object (wire or thin rope) moves easily in rotational motion and can have greater angular acceleration.

Tips to study Angular Acceleration

Angular acceleration is one of the most exciting chapters
in physics and can help you understand the mechanism behind the working of various objects in daily life. However, to understand the topic in-depth, here are a few steps you should take.

1. Read this article till you understand all the concepts stated here very well.

2. If students face difficulty in understanding something, you can ask us in the comments. You can also download ’s app and get a more clear understanding of topics.

3. Practice problems. Do not directly jump to tough problems. Start with simple questions of angular acceleration and gradually move to difficult conceptual questions.

4. Create your own revision notes after understanding this topic well. It will help you remember and write well in exams.

Solved Questions Angular Acceleration Formula

1) If the Body’s Angular Velocity in Rotational Motion Changes from [frac{Pi }{2}] rad/s to [frac{3Pi }{4}] in 0.4 sec. Find the Angular Acceleration.

Solution: 

 ω 1 = [frac{Pi }{2}] rad/s, ω2 = [frac{3Pi }{4}] rad/s, ∆t = 0.4

so by applying the formula for angular acceleration 

α= ∆ω/∆t = ω1 – ω2/∆t = π/4-3π/4 / 0.4 = [frac{5Pi }{8}] rad/s²  

2) The Angular Displacement of an Object in Rotational Motion is Usually Considered to be Depending on the Time t According to the Following Relation-

θ=2π t³ – -rt² + 3π – – 6, where θ is in rad and time in sec. Find angular acceleration at time t=2 sec.

Applying one of the formulas for angular acceleration angular velocity,

 

ω=dθ/dt = 6π t² – -2 π t + 3π rad

α=dω/dt = 12π t – -2π rad/s²

At t=2 sec, αt= 2s, 12π х 2 -2π = 22π rad/s²

The above examples are better to understand the angular acceleration. In two dimensions, angular acceleration is a pseudoscalar whose sign is taken to be positive if the angular speed increases counterclockwise or decreases clockwise. It is to be taken negatively if the angular speed increases clockwise and decreases counterclockwise.

In three dimensions, angular acceleration is a pseudovector.

 

In the case of rigid bodies, angular acceleration must be caused by a net external torque. This is not the same in the case of non-rigid bodies.

3. The radius of the tire of a car is about 0.35 meters. The car accelerates onto a straight path from rest at 2.8 m/s². Find the angular acceleration, both magnitude, and direction, of the front passenger-side tire?

Solution:
The angular acceleration is related to linear acceleration by the following equation.

α=a/r

In this case, a = 2.8 m/s²

and r = 0.35 meters.

Substituting these quantities into the equation, we get

α = a/r

= 2.8/0.35

= 8.0 rad/s²

By the use of the right-hand rule, we find that the direction of the angular acceleration is to the left side of the car when facing the direction in which the car is moving.

Physics App for Students

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These days, a trend of using the Physics App as a study resource has become popular. Many app builders do their best in reaching their study materials to the students worldwide. Now, the confusion arises in searching for reliable notes and concise solutions to numerical problems. 

Don’t worry; you made the right decision in downloading the ‘ App’ as your studying accomplice. Now, we will discuss the features of our App.

Best App for Physics Class 12

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The application covers the fundamental topics that are there in Class 12 board exams. These notes will also help you prepare for the premium entrance exams like IIT-JEE, NEET, and state-wise exams like KCET, EAMCET, and many more.

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With these features, we are sure; by now, you will consider App as the Best Physics Learning App. 

App: The Best App to Learn Live Online

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We are living at the very bottom of an invisible ocean which is called the atmosphere, which is a layer of gases that are surrounding our planet. Oxygen and Nitrogen types of gases which account for 99 % of the gases which are there in air which is also called dry air  along with carbon dioxide and helium and  argon, neon and even other gases which are making up a minute portions.

The atmosphere not only protects our environment from the dangerous things which are present in the planet earth but along with it it also provides us a layer which is responsible for balancing the temperature of our planet earth. The vapours of Water and the dust are also part of the atmosphere of Earth. Other planets and satellites like moons have very different atmospheres and when we observe that some have no atmospheres at all.

The bottom is said to be 30 kilometers  and 19 miles of the atmosphere contains around 98 percent of its mass. The air which is in the atmosphere is much thinner at high altitudes. The atmosphere is not in space.

Scientists say that there are many gases in our atmosphere that were ejected into the air by early volcanoes as well. At that time there would have been very little or in fact no free oxygen that surrounded the Earth. The oxygen which is Free oxygen consists of oxygen molecules not attached to another element like carbon to form carbon dioxide or hydrogen to form water.

The oxygen which is free oxygen may have been added to the atmosphere by primitive organisms which is  probably bacteria during photosynthesis. Photosynthesis is said to be a process where a plant or other autotroph is used to make oxygen and oxygen from carbon dioxide and water. Later on more complex forms of plant life were added with more oxygen to the atmosphere. To accumulate the oxygen in today’s atmosphere probably took millions of years.

Pressure 

The pressure of Atmospheric at a particular location is the force per unit area which is perpendicular to a surface determined by the weight of the vertical column of atmosphere above that location. On the planet Earth the units of air pressure are based on the internationally recognized standard atmosphere defined as atm, which is defined as 101.325 kPa that is 760 Torr or 14.696 psi. It is usually measured with a barometer.

Pressure of Atmospheric decreases with altitude increasing due to the diminishing mass of gas above. The pressure in the atmosphere which depends on the height defined as the one which is declined by the factor which is defined as e  that is an irrational number with a value of 2.71828 is known as the scale height and is denoted by capital H. For an atmosphere that has a uniform temperature for it the height which is scale height is directly proportional to the temperature and it is inversely proportional to the product of the molecular mean mass which of dry air and the local acceleration of gravity at that specific location. For atmospheres such a model, the pressure declines totally with increasing altitude. 

Scape of Atmosphere

The gravity of the Surface differs significantly among the planets.see the escape velocity distance from the Sun then we will see that it determines the energy available to heat atmospheric gas to the point where some fraction of its molecules’ thermal motion exceeds the planet’s. Thus if we see distant and cold Titan or Triton, to retain their atmosphere Pluto is able to despite their relatively low gravities.

there will always be some air that will be fast enough to produce a slow gas of leakage into space. The molecules which are Lighter molecules in nature move faster than the heavier molecules as we already know, along with the same thermal energy which is kinetic, and so the gases which are of low molecular weight are lost more easily than those of high molecular weight. It is said that the Mars and Venus planets may have lost much of their water when and  after being photo dissociated into gases like oxygen and hydrogen by solar ultraviolet radiation the hydrogen escaped. 

Composition of Atmosphere 

The atmosphere which is said to be the initial atmospheric composition of a planet is related to the temperature and the chemistry of the local solar nebula during planetary formation of interior gases which are subsequent. The atmosphere which is the original atmosphere started with a rotating disc of gases which later collapsed to form a series of spaced rings that condensed to form the planets. The planets such as Mars and Venus are primarily composed of carbon dioxide and with small quantities of nitrogen, oxygen, argon and traces of other gases as well.

The earth’s composition in the atmosphere is largely governed by the by-products of the life that it sustains. The air which is Dry from Earth’s atmosphere contains around 20.95% oxygen, 78.08% nitrogen, 0.93% argon, 0.04% and other gases which are said to be noble by volume, but generally if we see then a variable amount of vapours of water is also present on average about 1% at level of sea.

Bernoulli’s principle is also known as Bernoulli’s equation. It can be applied for fluids in an ideal state. We already know that pressure and density are inversely proportional to each other, which means, a fluid with slow speed will exert more pressure than fluid, which is moving faster. In this case, fluid refers to not only liquids but gases as well. Bernoulli’s principle forms the basis of many applications in our day-to-day lives.  

Some examples are – an airplane that tries to stay aloft, shower a certain billowing inward; this phenomenon happens in the case of rivers as well when there is a change in the width of the river. The speed of the water decreases in wider regions, whereas the speed of water increases in the narrower regions.

Most of you will think that the pressure within the fluid in the narrower parts will increase. However, contrary to the above statement, the pressure within the fluid in the narrower parts will decrease, and the pressure inside the fluid in the wider parts of the river will increase. Daniel Bernoulli, a Swiss Scientist discovered this concept while experimenting with fluid inside the pipes. He observed in his experiment that the speed of the fluid increases, but its internal pressure decreases. He referred to this concept as Bernoulli’s principle.

The concept is difficult to understand and quite complicated. It is possible to think that the pressure of water will increase in tighter spaces. Indeed, the pressure of water increases in tighter spaces, but pressure within the water will not increase. Thus, the surrounding of the fluid will experience an increase in pressure. The change in the pressure will also result in a change in the speed of the fluid.

Bernoulli’s Principle Formula

Bernoulli’s principle is a seemingly counterintuitive statement about how the speed of a fluid relates to its pressure. Many people across the globe believe that Bernoulli’s principle isn’t correct; however, this might be due to a misunderstanding about what Bernoulli’s principle says. Bernoulli’s principle states that within a horizontal flow of fluid, points of higher fluid speed will always have less pressure than the points of slower fluid speed.

Therefore, inside a horizontal water pipe that changes diameter, the regions where the water is moving fast will experience less pressure than the regions where the water is moving slowly. Bernoulli’s equation is usually written or expressed as follows: P1+1/2 ρv12+ ρgh1=P2+1/2 ρv22+ ρgh2 

Where ρ = density, g = gravitational acceleration, and v = velocity. 

In the equation mentioned above, the variables P1, v1, h1 denote the pressure, speed, and height of the fluid at point 1 respectively, whereas the variables P2, v2, h2 denote the pressure, speed, and height of the fluid at point 2 respectively.

Bernoulli’s Equation Derivation

For maintaining a constant volume flow rate, incompressible fluids have to increase their speed when they reach a narrow constricted section. The same accounts for why a narrow nozzle on a hose causes water to speed up. Now, something might be bothering you about this phenomenon. If the water is speeding up at a constriction, it must be gaining kinetic energy as well. So, from where is this extra kinetic energy coming? 

The only possible way of giving kinetic energy to something is by doing work on it. It is expressed by the work-energy principle.

W=ΔKE=1/2mv2f −1/2mv2i 

Where, W = work, ΔKE = change in kinetic energy, vf = final velocity, and vi = initial velocity. 

So, if a portion of the fluid is speeding up, something external to that portion of fluid must be doing work.

What is the force that causes work to be done on the fluid? The answer is, in most of the real-world systems, there are lots of dissipative forces that could be doing negative work; however, we’re going to assume for the sake of simplicity that these viscous forces are almost negligible, and there is a continuous and perfectly laminar (streamline) flow. 

Laminar or streamline flow implies that the fluid flows in parallel layers, that too, without crossing paths. In laminar streamline flow, there is no swirling or vortices in the fluid. Therefore, we’ll assume that we have no loss in energy due to dissipative forces. In such a case, what non-dissipative forces could be doing work on our fluid that causes it to speed up? The pressure from the surrounding fluid will be causing a force that can do work and speed up a portion of the fluid as well.

Principle of Continuity

The principle of continuity tells us that what flows into a defined volume in a defined time, minus what flows out of that volume at that time, must accumulate in that volume. If the accumulation is negative, then the material in that volume is being reduced. Bernoulli’s principle is a result of the law of conservation of mass. It fully describes the behavior of fluids in motion, along with a second equation – based on the second Newton’s laws of motion, and a third equation – based on the conservation of energy.

The Relation Between Conservation of Energy and Bernoulli’s Equation

The Bernoulli Equation can be expressed or defined as a statement of the conservation of energy principle appropriate for flowing fluids. The qualitative behavior that is usually labeled with the term “Bernoulli effect” is the decrease in the fluid pressure in regions where the flow velocity increases. The lowering of pressure in a constriction of a flow path may seem counterintuitive, but it seems less when you consider the pressure to be energy density. The kinetic energy must increase at the expense of pressure energy in the high-velocity flow through the constriction.

Bernoulli’s Equation at Constant Depth

The situation in which the fluid moves, but its depth is constant- that is h1=h2. Under that condition, Bernoulli’s equation becomes P1+1/2pv21 = P2+1/2pv22.

The situations in which fluid flows at a constant depth are so crucial that this equation is often called Bernoulli’s principle. It is Bernoulli’s equation for fluids at a constant depth. (Note again that this applies to a small volume of fluid as we follow it along its path).

Bernoulli’s Equation for Static Fluids

Let us consider the equation given below in which the fluid is static – that is, v[_{1}] = v[_{2}]=0. 

Bernoulli’s equation, in that case, is: P1+pgh1=P2+ ρgh2

We further simplify the equation by taking h2=0 (we can always choose some height to be zero, just as we often have done for other situations involving the gravitational force, and take all other heights to be relative to this). In that case, we get P2=P1+ ρgh1

This equation conveys that in static fluids the pressure increases with the increase in depth. As we go from point 1 to point 2 in the fluid, the depth increases by h1, and consequently, P2 is greater than P1 by an amount pgh1. In the simplest possible case, P1 is 0p at the top of the fluid, and we come to a familiar relationship as mentioned below:

P = ρgh

PEg= mgh

This equation includes the fact that the pressure due to the weig
ht of the fluid is ρ*g*h.