The index of refraction of the core of a typical fiber optic is ncore = 1. 46; the cladding has nclad = 1. 4. calculate the critical angles for the total internal reflection icrit and crit

a) U =  0 J

k = 0.383 J

E = 0.383 J

b) U = 0.0228 J

k = 0.155 J

E = 0.383 J

c) U = 0.1104 J

k = 0.272 J

E = 0.383 J

d) U = 0.248 J

k = 0.177 J

E = 0.383 J

The equations for kinetic energy is:

k= 1/2*m*[tex]v^{2}[/tex]

The equation for elastic potential energy is:

U= 1/2*ks*[tex]x^{2}[/tex]

Where,

m= mass of the block

v= velocity

ks= spring constant

x= displacement of the spring

(a)when compression= 0 cm

U= 1/2*ks*[tex]x^{2}[/tex]

U= 1/2*552*

= 0 J

Kinetic energy:

k= 1/2*m*[tex]v^{2}[/tex]

k= 1/2*(1.05)*

k= 0.383 J

Mechanical energy:

E= k + U

E= 0.383+0

E= 0.383 J

(b) spring potential = ?

U= 1/2* 457 N/m*[tex](0.01)^{2}[/tex]

U= 0.0228 J

Since the mechanical energy must remain constant, we may calculate the kinetic energy using the mechanical energy equation:

E= k + U

0.383= k + 0.0228

k= 0.383 - 0.228

k= 0.155

(c)spring constant when x= 0.02

U= 1/2*552*[tex](0.02)^{2}[/tex]

U= 0.1104 J

Using the equation of mechanical energy:

E= k +U

0.383= k+ 0.1104

k= 0.383 - 0.1104

k= 0.272 J

(d) U= 1/2*552*[tex](0.03)^{2}[/tex]

U= 0.2484 J

E= 0.383 J

k = E - U

k= 0.383- 0.206

k= 0.177

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The angular separation is [tex]4.88 * 10^{-5} rad[/tex]

What is angular distance formula?

The formula is θ=s/r, where, θ is Angular Displacement, s is the distance traveled by the body, and. r is the radius of the circle along which it is moving.

What is meant by angular resolution?

The angular resolving power (or resolution) of a telescope is the smallest angle between close objects that can be seen clearly to be separate. Resolution is limited by the wave nature of light.

The angular separation is calculated as given below.

θ = 1.220 λ/d

Where λ  is the wavelength and d is the diameter of the lens aperture.

θ1 = [tex]1.220 * \frac{600 * 10^{-9} }{1.5 * 10^{-2} }[/tex]

    =  4.88 × [tex]10^{-5}[/tex] rad

Therefore, The angular separation is 4.88 × [tex]10^{-5}[/tex] rad.

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It follows coulombs law.          

According to Coulomb’s law, the force of attraction or repulsion between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. It acts along the line joining the two charges considered to be point charges.

In Short: F ∝ q1q2/d2

where,

ε is absolute permittivity,

K or εr is the relative permittivity or specific inductive capacity

ε0 is the permittivity of free space.

K or εr is also called a dielectric constant of the medium in which the two charges are placed.

One coulomb of charge is that charge which when placed at rest in vacuum at a distance of one metre from an equal and similar stationary charge repels it and is repelled by it with a force of 9 x 109 newton.

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The average force exerted by the runner is 200N.

A force is an influence that has the power to alter an object's motion. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.

When a force is exerted across a distance to an item, work is accomplished. This implies that the total energy of an object will be impacted when a force is applied to it over a distance.

Work = Force x Distance

Force = work / distance

Force = 2000 J / 10 m

Force = 200 N

Hence, the average force exerted by the runner was 200N.

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Answer:

focal length

Explanation:

This describes focal length of the beam

The unit vectors along the three co-ordinate axes are described as. i > j > k > 1. is D. i = j = k = 1

A vector that has a volume of 1 is a unit vector. It is also known as a direction vector because it is generally used to denote the direction of a vector. The vectors i, j, k, stand the unit vectors along the x-axis, y-axis, and z-axis respectively.

There are three essential unit vectors which are commonly employed and these are the vectors in the direction of the x, y and z-axes. The unit vector in the direction of the x-axis is i, the unit vector in the direction of the y-axis is j and the unit vector in the demand of the z-axis is k.

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The direction angle of 4w- (2u v) is equal to 353.7°.

A vector's direction angle is the angle formed by the positive x-axis and the vector v. The arctangent of the ratio between the vertical and horizontal components of the vector, v=ai+bj, can be used to determine the direction angle,, of the vector.

Use the formula = arctan(y/x) to determine the direction of the vector v = (x, y), where is the smallest angle the vector makes with the horizontal axis and x and y are its component vectors.

The angle a vector creates with a horizontal line is used to determine the vector's direction. The formula:where x is the horizontal change and y is the vertical change, gives the direction angle of a vector.

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Two vectors are added geometrically (by drawing them), they arranged in such a way that Tail of one touching the head of the other .

A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity. Triangle law of vector addition is used to find the sum of two vectors when the head of the first vector is joined to the tail of the second vector.

Magnitude of the resultant sum vector R: R = √([tex]P^{2}[/tex] + 2PQ cos θ + [tex]Q^{2}[/tex])

According to the Parallelogram law of vector addition: If two vectors are considered to be the adjacent sides of a parallelogram, then the resultant of the two vectors is given by the vector that is diagonal passing through the point of contact of two vectors. drawn from the same point.

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If a violin string vibrates at 430 hz as its fundamental frequency,then the frequencies of the harmonics are 880, 1320, 1760

The frequency in physics is the number of waves passing a fixed location in a unit of time. It also indicates how many cycles or vibrations a body in periodic motion experiences in a given unit of time.

How frequently something occurs is what is meant by the word frequency. A person blinking their eyelids 47 times in a minute is an example of frequency. the quality or state of happening frequently.

Integer (whole-number) multiples of the fundamental frequency are used to define harmonics, which are voltages or currents that function at certain frequencies. This means that for a waveform with a fundamental frequency of 50 Hz, the second harmonic frequency would be 100 Hz (2 x 50 Hz), the third harmonic would be 150 Hz (3 x 50 Hz), etc.

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Explanation:

according to my understanding, the value of gravitational acceleration changes because;different planets have different gravitational pull.

for example you may ask yourself why is it that the gravitational acceleration is not the same on earth and the moon.

this is because the gravitational force acting on an object on earth is greater than the gravitational force acting on an object and the Moon .

You know the moon is located in the space and one can fly, stand,dance etc.

all because the gravitational acceleration is low.

as for me when the distance from the centre of the Earth increases,

the gravitational acceleration decreases.

A good example is given by the moon.

The moon is miles away from the Earth and its gravitational acceleration is quite low .hope you got me.

The velocity of the block when t == 2 s is 60.7 ft./sec.

Equations of Motion.

Here the friction is [tex]F_f = \mu_k N[/tex] = 0.2 N

[tex]+ \uparrow \sum F_y = ma_y; \quad N – 10 = \frac { 10 } { 32.2 }(0) \quad N = 10 lb \\ \begin{aligned} \underrightarrow{ + } \sum F_x = ma_x; \quad 8t^2 – 0.2(10 &) = \frac { 10 } { 32.2 }a \\ & a = 3.22(8t^2 – 2) ft/s^2 \end{aligned}[/tex]

Kinematics.

The velocity of the block as a function of t can be determined by

integrating dv = adt using the initial condition v = 4 ft./s at t = 0.

[tex]\int_{ 4 ft/s }^{ v } dv = \int_0^t 3.22(8t^2 – 2)dt \\ \begin{aligned} v – &4 = 3.22 (\frac 8 3 t^3 – 2t) \\ & v = \{8.5867t^3 – 6.44t + 4 \} ft/s \end{aligned}[/tex]

The displacement as a function of t can be determined by integrating

ds = vdt using

the initial condition s = 0 at t = 0

[tex]\int_0^s ds = \int_0^t (8.5867t^3 – 6.44t + 4)dt \\ s = \{2.1467t^4 – 3.22t^2 + 4t \} ft[/tex]

at t = 2 sec

s = 30 ft.

Thus, at s = 30 ft.,

[tex]\begin{aligned} v &= 8.5867(2.0089^3) – 6.44(2.0089) + 4 \\ &= 60.67 ft/s \\ &= 60.7 ft/s \end{aligned}[/tex]

Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move.

Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system.

Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. The study of how forces act on bodies falls within kinetics, not kinematics. For further details, see analytical dynamics.

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The sphere’s Electric potential energy is 1.6*[tex]10^{-6}[/tex]J

Given,

q=6. 5 µc, V=240 v,

We know that sphere’s Electric potential energy(E) = qV=6.5*[tex]10^{-6} *240[/tex]=1.6*[tex]10^{-6}[/tex]J

The configuration of a certain set of point charges within a given system is connected with the potential energy (measured in joules) known as electric potential energy, which is a product of conservative Coulomb forces. Two crucial factors—its inherent electric charge and its position in relation to other electrically charged objects—can determine whether an object has electric potential energy.

In systems with time-varying electric fields, the potential energy is referred to as "electric potential energy," but in systems with time-invariant electric fields, the potential energy is referred to as "electrostatic potential energy."

A tiny sphere carrying a charge of 6. 5 µc sits in an electric field, at a point where the electric potential is 240 v. what is the sphere’s potential energy?

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The 3kg of 20% of salt brine at 65 degrees Celsius has more enthalpy than the 5kg of 20% salt brine at 50 Degrees Celsius.

Enthalpy is defined as the total heat content of a system. The enthalpy is a measure of the total work which the system can do plus the internal energy of the system.

The enthalpy of the given solutions can be calculated as follows:

For the 3kg of 20% of salt brine at 65 degrees;

mass of salt = 3 * 20%  = 0.6 kg

specific heat capacity = 3.56kJ/kg*C

temperature change = 65°C

Enthalpy = 0.6 * 3.56 * 65

Enthalpy = 232 kJ

For the 5kg of 20% salt brine at 50 Degrees Celsius;

mass of salt = 5 * 20%  = 1 kg

specific heat capacity = 3.56kJ/kg*C

temperature change = 50°C

Enthalpy = 1 * 3.56 * 50

Enthalpy = 178 kJ

Therefore, the 3kg of 20% of salt brine at 65 degrees Celsius has more enthalpy.

In conclusion, the enthalpy or heat content of the solutions depends on the mass and temperature change.

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The answer is d) 20 m.

The depth of pond is 20 m if it seems to be 10 m.

The formula relating real depth and app. depth :

[tex]\boxed {A = \frac{R}{n}}}[/tex]

In this case, refractive index has to be an whole number for real depth to give a whole number for app. depth.

The current through the 10 Ω resistor is 0.586A which is connected with a resistor in series combination.

Voltage divides in a Series combination and current divides in a parallel combination.

Let the three resistors joined in parallel be R₁, R₂, R₃

where, R₁= 4 Ω

R₂ = 6 Ω

R₃ = 10 Ω

Given, a battery of 12V and a 2Ω resistor say r is series with the parallel combination.

Equivalent resistance(R) in parallel combination is:

1/R = 1/R₁ + 1/R₂ + 1/R₃

1/R = 1/4 + 1/6 + 1/10

On solving, R = 1.9 Ω

Now, the Equivalent resistance(R) of parallel combination is in series with r = 2Ω

Let Equivalent resistance of Series combination be R'

R' = R + r

R' = 1.9 + 2 Ω

R' = 3.9 Ω

Now let's calculate the voltage drop in the resistor r = 2Ω

v = i × r           where, i is the current in r and v is the voltage drop across r

v = 3.07 × 2

v = 6.14V

Voltage drop, V' across the Equivalent resistance(R) in parallel combination = Total voltage - voltage drop in the resistor r

V' = 12 - 6.14 V

V' = 5.86V

Now, the Voltage drop, V' across the Equivalent resistance(R) in parallel combination is same for all the three resistors R₁, R₂, R₃

So, Voltage is same in a parallel combination.

V' = I × R₃

5.86 = I × 10

I = 0.586A

Hence, The current through the 10 Ω resistor is 0.586A

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Answer:

The observations show a higher velocity than is predicted, mainly in the galaxy's outer regions, indicating that there is more mass in the exterior areas than we can see.

The observations show higher velocities than is predicted, mostly in the outer regions of the galaxy, indicating that there is more mass in the outer regions than we can see.

A galaxy is a collection of gravitationally bound stars, stellar remains, interstellar gas, dust, and dark matter. The name comes from the Greek word galaxias, which means "milky" in reference to the Milky Way galaxy, which houses the Solar System. Galaxies range in size from dwarfs, which have fewer than 100 million stars, to supergiants, which have 100 trillion stars around their galaxy's center of mass. Galaxies, on average, contain an estimated 100 million stars.

A galaxy can be classified as elliptical, spiral, or irregular based on how it appears to the human eye. Supermassive black holes are considered to be present in the centers of several. Sagittarius A*, the name given to the center black hole of the Milky Way, has a mass that is four million times that of the Sun.

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Power output will be  = 637.7448 W

Newton's third law states that when two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction. The third law is also known as the law of action and reaction.

Power Output means the average rate of electric energy delivery during one Metering

The upward force by which the bicycle is riding up will be equal and opposite to m*g*sin(10°) (using newtons third law)

Force (upward ) =  m*g*sin(10°)

given

v = 4.4 m/s

mass (m) = 85 kg

F (upward ) =  m*g*sin(10°)

ma =  m*g*sin(10°)

a = g*sin(10°)

  = 9.8 * sin(10°)  = 1.7052 m / [tex]s^{2}[/tex]

Power = work / time = Force . displacement / time = mass * acceleration * velocity

           = m * a * v

           = 85 * 1.7052 * 4.4

           = 637.7448 W

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The application of faraday's law to the existence (not the sign) of the induced voltage before you energize the primary coil

The magnitude of the emf generated in a circuit is proportional to the rate of change with time t of the magnetic flux that cuts across the circuit emf, according to this relationship, also known as Faraday's law of induction (to distinguish it from his laws of electrolysis).

According to Faraday's law of induction, when a magnetic field changes, a voltage results. This difference in electric potential can induce electric currents to flow.

The first faraday's law states that the amount of chemical change caused by a current at an electrode-electrolyte interface is proportional to the amount of electricity used, while the second law states that different substances can undergo different amounts of chemical change when the same amount of electricity is applied to them.

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The final velocity of the ball is  20.8 m/s. Option C

Now we have the equation;

v^2 = u^2 + 2gh

v = final velocity

u = initial velocity

a = acceleration

s = distance

v^2 = (11.4)^2 + (2 * 10 * 15.5)

v^2 = 129.96 + 310

v = √ 129.96 + 310

v = 20.8 m/s

b)

Given that;

R = u^2sin2θ/g

Where;

g = acceleration due to gravity

θ = acute angle

u = velocity

R = (60)^2 sin2(30)/10

R = 310 m

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The Capacitive reactance of the capacitor is 3.22kΩ.

To find the answer, we have to study about the Capacitive reactance.

                  [tex]C=9*10^{-8}F\\f=550Hz\\[/tex]

                      [tex]X_c=\frac{1}{2\pi fC}[/tex]

              [tex]X_c=\frac{1}{2\pi *550*9*10^{-8}} \\\\X_c=3.22*10^3Ohm.[/tex]

Thus, we can conclude that, the Capacitive reactance of the capacitor is 3.22kΩ.

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Energy is transferred.

Every time labour is performed, energy is transmitted, as shown by the definition of work in physics. Work is the result of the displacement's magnitude and the component of force acting in that direction.

What are 3 types of work done?

Work is the result of force and distance, or the force exerted over a specific distance. In other words, Work = Force x Distance.

Joules are used to measure work.

1. Positive Work: Positive work is when a force moves an object in that direction. The motion of a ball descending toward the earth while it is displaced in the direction of the force of gravity is an illustration of this type of labour.

2. Negative Work: The work is said to be negative if the force and the displacement are in the opposing directions. For instance, if a ball is thrown high, its displacement will also be upwards, while the force from the earth's gravity will be downward.

3. Zero Work: When the force and displacement directions are parallel to one another, there is no work done on the item by the force.

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Answer:Energy is transferred.

Explanation: Took the test and Passed

The mass of the electron is [tex]1.72\times 10^{-30}[/tex] Kg.

To calculate the mass of the electron we are using the formula,

[tex]m=\frac{m_{0} }{\sqrt{1-\frac{v^{2} }{c^{2} } } }[/tex]

Here we are given,

[tex]m_0[/tex]=The rest mass of an electron =  [tex]9. 11 \times 10^{-31}[/tex] kg.

v= The velocity of electron =  0. 85c.

c= The velocity of light = c.  (c=[tex]3\times 10^8[/tex] m/s)

We have to found the mass of an electron = m Kg.

Now we substitute the known values, we found that,

[tex]m=\frac{9. 11 \times 10^{-31} }{\sqrt{1-\frac{(0.85c)^{2} }{c^{2} } } }[/tex]

Or,[tex]m=\frac{9. 11 \times 10^{-31} }{\sqrt{1-(\frac{0.85c}{c})^2 } }[/tex]

Or,[tex]m=\frac{9. 11 \times 10^{-31} }{\sqrt{1-({0.85})^2 } }[/tex]

Or, [tex]m=1.72\times 10^{-30}[/tex] Kg.

From the above calculation we can conclude that, The mass of the electron is [tex]1.72\times 10^{-30}[/tex] Kg.

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The distance covered by the car before it stops is 98.58 m.

Force acting on the car will be

ma = -mg sinθ

where,

m = mass of the car

a = acceleration of the car

g = acceleration due to gravity

θ = angle of inclination

Given,

θ = 10°

Put the values in the above equation,

ma = -mg sinθ

a = -g sin 10°

a = -10 (0.173)

a = -1.73 m/s²

We know the initial velocity is 18.2m/s and when the car comes to a stop the final velocity becomes zero.

u = 18.2 m/s

v= 0 m/s

Using one of the kinematics equations,

v² - u² = 2as

0 - (18.2)² = 2 (-1.73) (s)

331.24 = 3.36 (s)

s = 98.58 m

Hence, the distance covered by the car before it stops is 98.58 m.

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Answer:

The answer to your question is more force

Explanation:

A consequence of more mass having more inertia is that more force is required to bring the helicopter to the same speed as the bullet

I hope this helps and have a good day!

A(n) closed system is one in which energy moves freely in and out, but no matter enters or leaves the system.

You can have an open or closed system: A system that is totally cut off from its surroundings is referred to as a closed system. We have opted to adopt this definition because it is one that is frequently used in the system literature.

A closed system is one that only permits the transfer of energy within or outside the system but not the transport of matter. For instance, a beaker of evaporating water with a closed top permits the flow of energy to the environment but prevents the evaporation of (matter) water.

closed systems are also referred to as systems that don't allow anything other than energy to enter or exit. A closed water bottle functions as a closed system in this instance.

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Electric potential energy of that charge at origin  = 40 V

Electric potential, the amount of work needed to move a unit charge from a reference point to a specific point against an electric field.

The electric potential energy of any given charge or system of changes is termed as the total work done by an external agent in bringing the charge or the system of charges from infinity to the present configuration without undergoing any acceleration.

Electric potential energy is defined as the total potential energy a unit charge will possess if located at any point in the outer space.

Potential energy at a point = change in electric potential to bring it from infinity to that point

Potential energy = Potential at that point - Potential at infinity

conventionally , potential at infinity is taken as zero

Potential energy = Potential at that point

hence , Potential energy of that charge at origin = Electric Potential at the origin

Potential energy of that charge at origin  = 40 V

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By Wien's displacement law we can conclude that, the peak wavelength emitted by the sun for 5800K temperature is 499nm.

To find the answer, we have to know about Wien's distribution law.

             [tex]wavelength*T=2.898*10^{-3}mK\\wavelength=\frac{2.898*10^{-3}mK}{5800K}=499nm.[/tex]

Thus, by Wien's displacement law we can conclude that, the peak wavelength emitted by the sun for 5800K temperature is 499nm.

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When the light turns from green to yellow while you are already in the intersection, proceed through the intersection at a safe speed.

To find the answer, we have to study more about the importance of traffic signals.

Thus, we can conclude that, When the light turns from green to yellow while you are already in the intersection, proceed through the intersection at a safe speed.

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The experiment's time period is unaffected by the change in amplitude in either experiment.

Time period is provided by:

[tex]T= 2\pi \sqrt{\frac{m}{k} }[/tex]

where,

T = time period

m = mass

k = spring constant

According to the formula, the only factors affecting the time period in a simple harmonic motion (SHM) are the object's mass and the spring constant . The time period will adjust in line with any adjustments made to the object's mass or spring constant.

Pendulum oscillations are an illustration of simple harmonic motion. Take into consideration a spring that has a fixed end. It is in its equilibrium position if no force is applied to it. Now, if we pull it outwards, the string exerts a force that is pointed in the direction of the equilibrium position.

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According to the solar nebula theory, the common direction of revolution and rotation for most objects in the solar system is because most objects in the Solar System have a common direction of revolution and rotation because they formed from the same rotating gas cloud.

The nebular theory states that our solar system formed from the gravitational collapse of a giant interstellar gas cloud—the solar nebula.

In nebula hypotheses its been said that solar system formed at the same time as the Sun . The nebular hypothesis is the idea that a spinning cloud of dust made of mostly light elements, called a nebula, flattened into a protoplanetary disk, and became a solar system consisting of a star with orbiting planets

Laplace theorized that the Sun originally had an extended hot atmosphere throughout the Solar System, and that this protostar cloud cooled and contracted. As the cloud spun more rapidly, it threw off material that eventually condensed to form the planets.

Since , Most objects in the Solar System have a common direction of revolution and rotation because they formed from the same rotating gas cloud.

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