a) 6.25 rad/s
The law of conservation of angular momentum states that the angular momentum must be conserved.
The angular momentum is given by:
[tex]L=I\omega[/tex]
where
I is the moment of inertia
[tex]\omega[/tex] is the angular speed
Since the angular momentum must be conserved, we can write
[tex]L_1 = L_2\\I_1 \omega_1 = I_2 \omega_2[/tex]
where we have
[tex]I_1 = 2.25 kg m^2[/tex] is the initial moment of inertia
[tex]\omega_1 = 5.00 rad/s[/tex] is the initial angular speed
[tex]I_2 = 2.25 kg m^2[/tex] is the final moment of inertia
[tex]\omega_2[/tex] is the final angular speed
Solving for [tex]\omega_2[/tex], we find
[tex]\omega_2 = \frac{I_1 \omega_1}{I_2}=\frac{(2.25 kg m^2)(5.00 rad/s)}{1.80 kg m^2}=6.25 rad/s[/tex]
b) 28.1 J and 35.2 J
The rotational kinetic energy is given by
[tex]K=\frac{1}{2}I\omega^2[/tex]
where
I is the moment of inertia
[tex]\omega[/tex] is the angular speed
Applying the formula, we have:
- Initial kinetic energy:
[tex]K=\frac{1}{2}(2.25 kg m^2)(5.00 rad/s)^2=28.1 J[/tex]
- Final kinetic energy:
[tex]K=\frac{1}{2}(1.80 kg m^2)(6.25 rad/s)^2=35.2 J[/tex]
To find the final angular speed, we can apply the conservation of angular momentum. The initial and final kinetic energies can be calculated using a formula involving the moment of inertia and angular velocity.
Explanation:To solve this problem, we can apply the principle of conservation of angular momentum. When the figure skater pulls in her arms, her moment of inertia decreases, causing her angular velocity to increase according to the equation:
Ii * ωi = If * ωf
where Ii and If are the initial and final moments of inertia, and ωi and ωf are the initial and final angular velocities, respectively.
a) Plugging in the given values:
2.25 kg·m2 * 5.00 rad/s = 1.80 kg·m2 * (ωf)
Solving for ωf, we find that the final angular speed is 6.25 rad/s.
b) To calculate the initial and final kinetic energies, we can use the equation:
K.E. = (1/2) * I * ω2
Substituting the values into the equation:
Initial K.E. = (1/2) * 2.25 kg·m2 * (5.00 rad/s)2
Final K.E. = (1/2) * 1.80 kg·m2 * (6.25 rad/s)2
Calculating, we find that the initial kinetic energy is 28.125 J and the final kinetic energy is 42.19 J.
Learn more about Angular Momentum here:https://brainly.com/question/37906446
#SPJ3
Susie rubbed the plastic wand with a silk cloth. She brought the wand close to the top of the electroscope. Note what happened when she did this. How did Susie make the initial static charge that started this process?
Answer:
She caused friction
Explanation:
(I'm not a 100% sure but, whatever) When you rub something up against another object, it causes friction. An example is rubbing a balloon to your hair. It sticks to your hair because it has (I think) like charges. Hope this helped
Answer:
She got initial negative charge on wand due to friction.
Explanation:
When Susie rubbed silk with the plastic wand, she makes static negative charge on the plastic wand due to friction. When she brought this negatively charged wand near the electroscope, electrons are pushed down into the electroscope. As a result, conducting rod and foil of electroscope become negatively charged but, net charge on electroscope is still zero.
The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 6-hour period. What is a cosine function that models this reaction?
Answer:
Explanation:
The general cosine wave function is:
y = A cos(ωt + φ) + B
where A is the amplitude, ω is the frequency, φ is the phase offset, and B is the vertical offset.
The temperature ranges from -10 to 50, so the magnitude of the amplitude is:
|A| = (50 − -10) / 2
|A| = 30
It's at its lowest point at t=0, so the sign of the amplitude is -1:
A = -30
The lowest point, -10, is 20 more than the amplitude, so the vertical offset is:
B = 20
The reaction completes 1 cycle in 6 hours, so f = 1/6. ω = 2πf, so:
ω = 2π (1/6)
ω = π/3
So the function is:
y = -30 cos(π/3 t) + 20
Alternatively, instead of a negative sign, we could have added a phase shift of π:
y = 30 cos(π/3 t + π) + 20
Either of these answers is correct.
A 10-cm-diameter parallel-plate capacitor has a 1.0 mm spacing. the electric field between the plates is increasing at the rate 1.0 * 106 v/m s. what is the magnetic field strength (a) on the axis, (b) 3.0 cm from the axis, and (c) 7.0 cm from the axis?
(a) 0
The magnetic field strength insidea a parallel-plate capacitor with changing electric field can be found by applying Ampere's law:
[tex](2\pi r) B = \mu_0 I_D[/tex] (1)
where
[tex](2\pi r)[/tex] is the circumference of the circular line of radius r with axis coincident to the axis of the capacitor, used to calculate the magnetic field
B is the strength of the magnetic field
[tex]I_D[/tex] is the displacement current enclosed by the area of the circular line mentioned above, and it is equal to
[tex]I_D = \epsilon_0 \frac{d\Phi_E}{dt} = \epsilon_0 (\pi r^2) \frac{dE}{dt}[/tex] (2)
where
[tex]\frac{d\Phi_E}{dt}[/tex] is the rate of change of electric flux through the area enclosed by the line
[tex]\frac{dE}{dt}=1.0\cdot 10^6 V/m[/tex] is the rate of change of the electric field
Rewriting eq.(1), we find
[tex]B = \frac{\mu_0 \epsilon_0 r}{2}\frac{dE}{dt}[/tex]
which is valid for r < R (where R=5.0 cm is the radius of the plates of the capacitor).
In this part of the problem,
r = 0
since we are on the axis; so substituting r=0 inside the formula above, we find
B(0) = 0
(b) [tex]1.67\cdot 10^{-13}T[/tex]
In this part, we have
r = 3.0 cm = 0.03 m
The formula used in part (a) is still valid since r<R, so we can directly use it to find the magnitude of the magnetic field:
[tex]B = \frac{\mu_0 \epsilon_0 r}{2}\frac{dE}{dt}=\frac{(4\pi\cdot 10^{-7}H/m)(8.85\cdot 10^{-12}F/m)(0.03 m)}{2}(1.0\cdot 10^6 V/m)=1.67\cdot 10^{-13}T[/tex]
(c) [tex]1.98\cdot 10^{-13} T[/tex]
In this part, we have
r = 7.0 cm = 0.07 m
so here
r > R
therefore we need to substitute [tex](\pi r^2)[/tex] with [tex](\pi R^2)[/tex] in eq. (2), since the area through which the flux is calculated is only [tex](\pi R^2)[/tex] (there is no electric field outside the area of the capacitor). So we find
[tex]I_D = \epsilon_0 (\pi R^2) \frac{dE}{dt}[/tex]
and therefore
[tex]B = \frac{\mu_0 \epsilon_0 R^2}{2r}\frac{dE}{dt}=\frac{(4\pi\cdot 10^{-7}H/m)(8.85\cdot 10^{-12}F/m)(0.05 m)^2}{2(0.07 m)}(1.0\cdot 10^6 V/m)=1.98\cdot 10^{-13} T[/tex]
The magnitude of the magnetic field 3 cm from the axis is [tex]1.67\times 10^{-13} \rm \ T[/tex].
What is a magnetic field?It is a vector field in which ferromagnetic objects and moving charges experience an influence.
The magnitude of the magnetic field can be calculated by the formula,
[tex]B =\dfrac { \mu _0 \epsilon_0 r} 2\times \dfrac {dE}{dt}[/tex]
Where,
μ - magnetic permeability = [tex]4\pi \times 10^{-7}{\rm \ H/m}[/tex]
r - distance = 3 cm
[tex]\dfrac {dE}{dt}[/tex] - rate of electic field = [tex]1.0 \times 10^6 \rm v/m s.[/tex]
Put the values in the formula,
[tex]B =\dfrac { 4\pi \times 10^{-7}{\rm \ H/m} (8.85\times 10^{-12}) (0.03)} 2\times(1.0\times 10^6)\\\\B = 1.67\times 10^{-13} \rm \ T[/tex]
Therefore, the magnitude of the magnetic field 3 cm from the axis is [tex]1.67\times 10^{-13} \rm \ T[/tex].
Learn more about the magnetic field:
https://brainly.com/question/19542022
What is the value of x in the equation below 1+2e^x+1=9
Explanation:
We are given this equation and we need to find the value of [tex]x[/tex]:
[tex]1+2e^x+1=9[/tex] (1)
Firstly, we have to clear [tex]x[/tex]:
[tex]2e^x=9-1-1[/tex]
[tex]2e^x=7[/tex]
[tex]e^x=\frac{7}{2}[/tex] (2)
Applying Natural Logarithm on both sides of the equation (2):
[tex]ln(e^x)=ln(\frac{7}{2})[/tex] (3)
[tex]xln(e)=ln(\frac{7}{2})[/tex] (4)
According to the Natural Logarithm rules [tex]xln(e)=x[/tex], so (4) can be written as:
[tex]x=ln(\frac{7}{2})[/tex] (5)
Finally:
[tex]x=1.252[/tex]
Jackson and Mia want to do an experiment to determine how the temperature of water affects how much salt can be dissolved in it
In what order should they perform the following steps?
Step 1: Bring the water in one of the beakers to the boiling point.
Step 2: Pour equal amounts of water into two identical beakers.
Step 3: Record how many half-teaspoons of salt are completely dissolved in each beaker
Step 4: Gradually put salt into the water of each beaker, a half-teaspoon at a time.
Answer:
First- step 2
Second- step 1
Third- step 4
Fourth- step 3
Explanation:
You need to first make sure you have water or you can’t do any dissolving. Then you need boil it or nothings going to happen to the salt. And then you you can do the fourth step without doing the dissolving first hope this helped :)
An experiment is to determine how the temperature of water affects how much salt can be dissolved in it must be carried out in the correct sequence of steps.
In this experiment, the dependent variable is the amount of salt dissolved in the water, the independent variable is the temperature of the water. The correct sequence of steps in which the experiment should be carried out is;
Step 1: Pour equal amounts of water into two identical beakers. Step 2: Gradually put salt into the water of each beaker, a half-teaspoon at a time.Step 3: Record how many half-teaspoons of salt are completely dissolved in each beaker Step 4: Bring the water in one of the beakers to the boiling point.Above are outlined the correct sequence of steps to carry out the experiment.
Learn more: https://brainly.com/question/967776
A parallel-plate capacitor is formed from two 1.0 cm times 1.0 cm electrodes spaced 2.9 mm apart. The electric field strength inside the capacitor is 1.0 times10^{6} N/C. What is the charge (in nC) on positive electrode?
Answer:
0.89 nC
Explanation:
The strength of the electric field inside a parallel plate capacitor is given by
[tex]E=\frac{Q}{A \epsilon_0}[/tex] (1)
where
Q is the charge stored on one plate
A is the area of one plate
[tex]\epsilon_0[/tex] is the vacuum permittivity
For this problem, we have
[tex]E=1.0\cdot 10^6 N/C[/tex] is the electric field strength
the area of one plate is
[tex]A=1.0 cm\cdot 1.0 cm=(0.01 m)(0.01 m)=1\cdot 10^{-4} m^2[/tex]
Solving the formula (1) for Q, we find the charge on the positive electrode:
[tex]Q=EA\epsilon_0=(1.0\cdot 10^6 N/C)(1\cdot 10^{-4} m^2)(8.85\cdot 10^{-12} F/m)=8.85\cdot 10^{-10}C=0.89 nC[/tex]
Electric field exerts a force on all charged particles. The charge on the positive electrode is 8.854 x 10⁶ C.
What is an electric field?An electric field can be thought to be a physical field that surrounds all the charged particles and exerts a force on all of them.
Given to us
Plate dimensions = 1.0 cm times 1.0 cm
Area of the plate = 0.0001 m²
Distance between the two plates, d = 2.9 mm = 0.0029 m
Electric field strength, [tex]\overrightarrow E[/tex] = 1.0 x 10⁶ N/C
We know that electric field inside a parallel plate capacitor is given as,
[tex]E = \dfrac{Q}{A\epsilon_0}[/tex]
Substitute the value,
[tex]1 \times 10^6 = \dfrac{Q}{0.0001\times 8.854 \times 10^{-12}}\\\\Q = 8.854 \times 10^{-10} \rm\ C[/tex]
Hence, the charge on the positive electrode is 8.854 x 10⁶ C.
Learn more about the Electric field:
https://brainly.com/question/4440057
Which two processes can generate energy to help a star or gas cloud maintain its internal thermal pressure?
A star is born when the material of a nebula collapses due to the gravitational force of its elements. Converting this later into the nucleus of the new star, composed of hydrogen.
Then, when this nucleus has reached sufficiently high density and temperature, it becomes helium by means of nuclear fusion (union of two light atoms), releasing energy in the process, which is the cause of the great luminosity of the star.
In other words, stars generate their own energy, in a process in which there is a balance between the gravitational pressure that compresses (contracts) matter and raises its temperature sufficiently for nuclear reactions to start, generating pressure in the opposite direction to the gravitational force by the heat produced in the reaction.
So, these nuclear reactions expand the star for most of its life, as long as this equilibrium exists.
Why is wind energy considered clean energy?
Answer:Wind power is a clean energy source that we can rely on for the long-term future. A wind turbine creates reliable, cost-effective, pollution free energy. ... Because wind is a source of energy which is non-polluting and renewable, the turbines create power without using fossil fuels.
_______________Is the distance traveled during a specific unit of time.
Answer:
Speeed
Explanation:
The speed of an object is defined as the rate of change of distance:
[tex]v=\frac{d}{t}[/tex]
where
d is the distance covered by the object
t is the amount of time needed to cover that distance
Speed is measured in meters per second (m/s). It should be noted that speed is a scalar quantity, so it only has a magnitude (and no direction).
help fast
at 8:00 am you leave home and walk 0.5 km to a friends house at 11:30 am u return home then travel by car to the mall which is 10km away and arrive at 11:45 am what is the total distance
A)2.8 km/h
B)10km
C)10.5km
D)11km
Answer: 11 Km
Explanation: You walk 0.5 to the friends and 0.5 back. This adds up to 1. Then you drive 10 Km to the mall. When you add 1 and 10 you get 11! Hope this helps!
The is the the distance between two crests or two troughs on a transverse wave. It is also the distance between compressions or the distance between rarefactions on a longitudinal wave.
Answer:
Wavelength
Explanation:
The wavelength of a transverse wave (where the oscillation occurs perpendicular to the direction of propagation of the wave) is defined as the distance between two consecutive crests ot two consecutive troughs.
In a longitudinal wave, where the oscillation occurs parallel to the direction of propagation of the wave, the wavelength is defined as the distance between two consecutive compressions or between two consecutive rarefactions.
Other important definitions for a wave are:
- Frequency: the number of complete cycles per second
- Period: the time needed for one complete cycle to occur
- Amplitude: the distance between the equilibrium position and the maximum displacement of the wave
Answer:
wavelength
Explanation:
The small currents in axons corresponding to nerve impulses produce measurable magnetic fields. A typical axon carries a peak current of 0.040 ?A.
What is the strength of the field at a distance of 1.6 mm ?
Answer:
[tex]5.0\cdot 10^{-12}T[/tex]
Explanation:
We can think the axons as current-carrying wires
The strength of the magnetic field produced by a current-carrying wire is
[tex]B=\frac{\mu_0 I}{2\pi r}[/tex]
where
[tex]\mu_0[/tex] is the vacuum permeability
I is the current
r is the distance from the wire
In this problem we have
[tex]I=0.040 \mu A = 0.04\cdot 10^{-6} A[/tex]
r = 1.6 mm = 0.0016 m
So the strength of the magnetic field is
[tex]B=\frac{(4\pi \cdot 10^{-7}H/m)(0.04\cdot 10^{-6} A)}{2\pi (0.0016 m)}=5.0\cdot 10^{-12}T[/tex]
The mass of a proton is approximately equal to
Answer:
[tex]1.6726\cdot 10^{-27} kg[/tex]
Explanation:
The three main particles that make an atom are:
- Proton: its mass is [tex]1.6726\cdot 10^{-27} kg[/tex], it carries an electric charge of +e ([tex]e=1.6\cdot 10^{-19}C[/tex]), and it is located in the nucles of the atom
- Neutron: its mass is [tex]1.6749 \cdot 10^{-27}kg[/tex], it carries no electric charge, and it is also located in the nucleus of the atom
- Electron: its mass is [tex]9.1094 \cdot 10^{-31}kg[/tex], it carries an electric charge of -e ([tex]e=1.6\cdot 10^{-19}C[/tex]), and it is located outside the nucleus
please help on this one?
How do the nuclei of different isotopes of an element vary?
Because isotopes of an element have a different number of neutrons, they also have different mass numbers.
(PLEASE HELP! Will give Brainliest Answer)
The coaster below starts from rest at point A.
It has a mass of 872 kg. There is no friction or air resistance.
Point A is 50 meters above ground. Point B is 20 meters above ground.
Calculate the speed of the coaster at point B.
A) 24 m/s
B) 50 m/s
C) 20 m/s
Answer:
B
Explanation:
872 / 20 = 43
Many sophisticated cameras have zoom lenses. When you select the telephoto setting, the objects in front of you appear much closer. In this setting, (A) the focal length of the lens is shorter than normal. (B) the aperture of the lens is larger than normal. (C) the focal length of the lens is longer than normal. (D) the aperture of the lens is smaller than normal.
The amswer is a i think cuz it make semse
The equation h=80t-16t^2 models the height h in feet reached in t seconds by an object propelled straight up from the ground at a speed of 80 ft/s. use the discriminant to find whether the object will ever reach a height of 90 ft
The object will reach a height of 90ft
To solve this exercise we are going to use the discriminant of the quadratic polynomial ax²+bx+c=0, which is b²-4ac.
If the discriminant is negative, then there are no real solutions to the equation.
If the discriminant is zero, there is only one solution.
If the discriminant is positive, there are two real solutions.
We have the equation h(t)=18t-16t² which describes the model of the height h (feet) reached in t (seconds) by an object propelled straight up from the ground at a speed of 80 ft/s. We want to use the discriminant to find whether the object will ever reach a height of 90ft.
First, we have to rewrite the equation to the form ax²+bx+c=0 and we know the height that is possible to reach for the object h=90ft.
90 = 80t-16t² ----------> -16t²+80t-90=0
Using the discriminan equation D = b²- 4ac.
From the quadratic polynomial -16t²+80t-90=0, we have a = -16, b = 80, and c = -90
D = (80)² - 4 (-16)(-90)
D = 6400 - 5760 = 640
Since the discriminant D is positive, the object will reach a height of 90ft.
Please help on this one?
Kepler's laws follow which law discovered by Sir Isaac Newton?
Kepler found that the orbits of the planets flowed three laws (rayed disk),(black dot) and maybe (symbols) hopes this helps out for you
Kepler took Brahe's detailed descriptions and measurements of the motion of the planets in the sky over many years, and derived his 3 laws of Planetary Motion based purely on what Brahe saw.
A hundred years AFTER Kepler, Newton proposed his Law of Universal Gravitation.
Using his own Law of Universal Gravitation, along with his laws of motion, Newton showed that IF his "laws" were correct, then planets HAVE TO move exactly according to Kepler's laws. (He had to invent Calculus in order to demonstrate this.)
This was an awesome, powerful confirmation of Kepler's work and Newton's work. Boat uvum.
In my Physics courses, I used to be able to take Newton's laws of gravity and motion, fold in some calculus and some geometry, mix until smooth, and derive Kepler's laws of planetary motion. But that was long ago, in a galaxy far away, and, sadly, ya don't get to use it very often as an Electrical Engineer. So I imagine it's still true, but I can't prove it now.
A simple pendulum consisting of a bob of mass m attached to a string of length L swings with a period T.
a.) If the bob's mass is doubled, approximately what will the pendulum's new period be?
b.) If the pendulum is brought on the moon where the gravitational acceleration is about g/6, approximately what will its period now be?
c.) If the pendulum is taken into the orbiting space station what will happen to the bob?
The answer to this question is b
The right question is
b.) If the pendulum is carried to the moon where the acceleration of gravity is around g / 6, what is the current period?
Further Explanation
A simple pendulum consists of a light string and a small ball (pendulum ball) with mass m hanging from the end of the rope. In analyzing the movement of a simple pendulum, the air friction force is ignored and the mass of the rope is so small that it can be ignored relative to the ball.
A simple pendulum consisting of a rope with a length L and a pendulum ball with mass m. The forces acting on the pendulum ball are the weight force (w = mg) and the FT string tension force. Gravity has a component of mg cos theta which is in the direction of the rope and mg sin theta which is perpendicular to the rope. The pendulum oscillates due to the presence of mg sin theta gravity component. Because there is no air friction, the pendulum oscillates along a circular arc with the same amplitude.
The requirement for an object to do Simple Harmonic Motion is if the recovery force is proportional to the deviation. If the recovery force is proportional to the deviation of x or the angle of the theta, the pendulum performs Simple Harmonic Motion.
The simple pendulum period can be determined using the equation:
T = 2n (sqrt m / k
We replace the effective force constant with mg / L
T = 2n (sqrt m / (mg / L))
T = 2n (sqrt L / g -> 0 small)
Simple Pendulum Frequency
f = 1 / T
f = 1 / 2n (sqrt L / g)
f = (1 / 2n) (sqrt g / L -> 0 small)
This is a simple pendulum frequency equation
Information :
T is the period, f is the frequency, L is the length of the rope and g is the acceleration due to gravity.
Learn More
Simple Pendulum https://brainly.com/question/12473773
Formula simple pendulum https://brainly.com/question/12644845
Detail
Class: High School
Subject: Physics
Keywords: pendulum, simple, formula
A ray in glass arrives at the glass-water interface at an angle of 48° with the normal. The refracted ray, in water, makes a 72° angle with the normal. The index of refraction of water is 1.33. Then the ray in glass is redirected so its new angle of incidence is 37°. What is the new angle of refraction in the water? Show all work.
Answer:
50.4°
Explanation:
Snell's law states:
n₁ sin θ₁ = n₂ sin θ₂
where n is the index of refraction and θ is the angle of incidence (relative to the normal).
When θ₁ = 48°:
n sin 48° = 1.33 sin 72°
n = 1.702
When θ₁ = 37°:
1.702 sin 37° = 1.33 sin θ
θ = 50.4°
The new angle of refraction in the water is [tex]50.35^{\circ}[/tex].
Given data:
The angle made by ray at glass-water interface is, [tex]\theta _{1} = 48^{\circ}[/tex].
The angle made by the refracted ray with the normal is, [tex]\theta_{2} = 72^{\circ}[/tex].
The index of refraction of water is, [tex]n=1.33[/tex].
The angle of incidence for the redirected glass is, [tex]\theta_{3} = 37^{\circ}[/tex].
The entire problem is based on the concepts of Snell's law, which says that the ratio of sine of angle of incidence to sine of angle of refraction is equal to the ratio of refractive index and incident index.
So on applying the Snell's law as,
[tex]n' \times sin \theta_{1} = n \times sin \theta_{2}[/tex]
Here, n' is the index of refraction of glass.
Solving as,
[tex]n' \times sin 48 = 1.33 \times sin 72\\\\n' = \dfrac{ 1.33 \times sin 72}{sin 48} \\\\n' =1.702[/tex]
For redirected condition, again apply the Snell' law as,
[tex]n' \times sin \theta_{3} = n \times sin \theta_{4}[/tex]
Here, [tex]\theta_{4}[/tex] is the new angle of refraction in the water.
Solving as,
[tex]1.702 \times sin 37 = 1.33 \times sin \theta_{4}\\\\sin \theta_{4} = \dfrac{1.702 \times sin 37}{1.33} \\\\\theta_{4} =sin^{-1}(0.770)\\\\\theta_{4} =50.35^{\circ}[/tex]
Thus, we can conclude that the new angle of refraction in the water is [tex]50.35^{\circ}[/tex].
Learn more about the Snell's law here:
https://brainly.com/question/24181353
The pole star, polaris, is nearby stationary and straight overhead when seen from the north pole. when viewed from the equator it
-- The 'pole star', Polaris, is always nearly stationary in the sky.
-- It's located almost straight overhead when seen from the north pole.
-- When viewed from the equator, Polaris is right on the northern horizon.
-- Looking from anywhere in the southern hemisphere (south of the equator), Polaris is below the horizon, and can't be seen at all.
A person who was born and raised in the southern hemisphere, and who has never crossed the equator, has never seen Polaris, the "North Star" !
Polaris, known as the pole star, appears nearly overhead at the North Pole. As one moves towards the equator, Polaris drops closer to the horizon and is directly on the northern horizon when viewed from the equator. This appearance changes due to Earth's rotation and the precession of the equinoxes, meaning Polaris won't always be the pole star.
Explanation:The pole star, Polaris, occupies a special position in the sky nearly aligned with Earth's rotational axis. At the North Pole, Polaris appears almost directly overhead. However, as one travels towards the equator, the angle at which Polaris is seen decreases. This is because the celestial sphere appears to turn around the Earth's axis, and Polaris is situated close to the north celestial pole. Thus, at the equator, Polaris is positioned right at the northern horizon, and as one goes further south,
it is no longer visible. Instead, one can observe the southern celestial pole. It is interesting to note that the close alignment of Polaris with the north celestial pole is temporary in the grand scheme of Earth's history due to the precession of the equinoxes. In the past, other stars, like Thuban, have served as the pole star, and in the future, Polaris will no longer hold that position.
A uniform solid sphere has a moment of inertia I about an axis tangent to its surface. What is the moment of inertia of this sphere about an axis through its center?a) 7/5 Ib) 3/5 Ic) 2/5 I
d) 1/7 I
Answer:
2/7 I
Explanation:
The theorem of parallel axis states that the moment of inertia of a body about a certain axis z' is equal to the moment of inertia of the body about the axis passing through the centre, z, plus the product between the mass of the body (M) and the square of the distance (r) between the two axis:
[tex]I_z' = I_z + Mr^2[/tex] (1)
For a solid sphere, the moment of inertia about the axis passing through the centre is
[tex]I_z=\frac{2}{5}MR^2[/tex] (2)
where R is the radius of the sphere.
The moment of inertia about an axis tangent to the surface then will be (applying (1) using r=R):
[tex]I = \frac{2}{5}MR^2 + MR^2 = \frac{7}{5}MR^2[/tex] (3)
The problem asks us to rewrite [tex]I_z[/tex], the moment of inertia about the centre, in terms of I, the moment of inertia about the axis tangent to the surface. We can do it by rewriting (2) as follows:
[tex]MR^2 = \frac{5}{2}I_z[/tex]
And substituting this into (3):
[tex]I=\frac{7}{5}(MR^2 )=\frac{7}{5}(\frac{5}{2} I_z) = \frac{7}{2}I_z\\I_z = \frac{2}{7}I[/tex]
The moment of inertia of a uniform solid sphere about an axis through its center is 3/5 times the moment of inertia of the sphere about an axis tangent to its surface. This is calculated using the parallel axis theorem.
The correct option is b.
Explanation:In physics, the moment of inertia of a sphere about an axis through its center is determined using the parallel axis theorem. The formula of the parallel axis theorem is: Icm = I + Mh2, where Icm is the moment of inertia about an axis through the center of mass, I is the moment of inertia about a parallel axis through the edge of the sphere, M is the mass of the sphere, and h is the distance between the two axes.
In this case, the sphere is uniform, so its center of mass is in its geometric center. The axis through the edge of the sphere is a distance of the radius of the sphere away from the axis through its center, so h = r. Also, in a solid sphere, the moment of inertia, Icm, about an axis through its center is (2/5)MR2.
With these values substituted into the formula, we have: (2/5)MR2 = I + MR2.
From this it can be deduced that I = 2/5 MR2 - MR2 = -(3/5) MR2. So the moment of inertia of this sphere about an axis through its center is (3/5) times smaller than the moment of inertia about an axis tangent to its surface.
This gives us an answer of choice b) 3/5 I.
Learn more about Moment of Inertia here:https://brainly.com/question/30051108
#SPJ3
The energy absorbed or released during a reaction in which a substance is produced is called the
the answer is bond energy but I am not pretty sure
When did robert fulton invent the steamboat
Answer:
1807
Explanation:
Robert Fulton (1765–1815) was an American engineer and inventor who is widely known for developing a commercially successful steamboat called Clermont. In 1807, that steamboat took passengers from New York City to Albany and back again, a round trip of 300 miles, in 62 hours.
Robert Fulton invented the steamboat engine in 1807, significantly improving water transportation with the Clermont on the Hudson River, and facilitating economic growth and western settlement.
Explanation:Robert Fulton invented the steamboat engine which was utilized in his first successful commercial steamboat, the Clermont, in 1807. Operating on the Hudson River, the Clermont was influential in transforming water transportation by allowing more reliable and quicker travel independent of wind. It traveled from New York City to Albany in a mere 32 hours. Fulton's innovation prompted widespread economic development, particularly in the Mississippi River Valley, and revolutionized the settlement of the West. By the 1830s, over a thousand steamboats were in operation. Yet, steamboats were prone to dangers such as boiler explosions, which eventually led to safety regulations.
PLEASE HELP ASAP! THANKS!
Why is it a rare occasion to see a solar eclipse from your home?
Answer:
It is very rare to see a solar eclipse from your home, because the Earth, Sun, and the moon need to align just right. Not everyone in the world can view a solar eclipse, only some area can. A solar eclipse is where the moon blocks out the sun. If you think about it: Let's say you live in Florida, U.S.A. You may see the moon coming in front of the sun, but if you lived in California or sumthin', the moon and the sun wouldn't be aligned to form a solar eclipse. It all depends on location... so it is rare to see one.
The material through which a mechanical wave travels is
The medium is the main factor that differentiates a mechanical wave from an electromagnetic wave, since the first can not propagate without its existence, while the second can propagate regardless of whether the medium exists or not.
In addition, it is the medium that will define, the propagation speed of the wave, according to its specific physical characteristics.
The distance traveled by an object divided by the time it takes to travel that distance is called
Answer:
Speed
Explanation:
- Speed is a scalar quantity that represents the rate of change of distance. It is calculated as
[tex]v=\frac{d}{t}[/tex]
where
d is the distance travelled by the object (regardless of its direction)
t is the time elapsed
The speed is measured in meters per second (m/s). We can also notice that speed is different from velocity: in fact, speed is a scalar quantity (magnitude only), while velocity is a vector quantity (magnitude+direction).
Are light waves longitudinal or transverse
Answer:
Transverse
Explanation:
There are two types of waves, according to the direction of their oscillation:
- Transverse waves: in a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. Examples of transverse waves are electromagnetic waves
- Longitudinal waves: in a longitudinal wave, the direction of the oscillation is parallel to the direction of motion of the wave. Examples of longitudinal waves are sound waves.
Light waves corresponds to the visible part of the electromagnetic spectrum, which includes all the different types of electromagnetic waves (which consist of oscillations of electric and magnetic fields that are perpendicular to the direction of propagation of the wave): therefore, they are transverse waves.