An explanation is greatly apreciated.
A particle's potential energy as a function of position is given by U=1x³-4x²-9x + 16, with a in meters and U in joules. Part A Find the positions of any stable and unstable equilibria. Express your
Answers
The positions of the stable and unstable
equilibria
are as follows:
Stable equilibrium: x = 9
Unstable equilibrium: x = -1/3
To find the positions of stable and unstable equilibria, we need to analyze the behavior of the
potential
energy function U(x).
Stable equilibria occur at points where the potential energy is at a minimum, and unstable equilibria occur at points where the potential energy is at a maximum.
Given the potential
energy
function U(x) = x³ - 4x² - 9x + 16, we can find the positions of stable and unstable equilibria by finding the critical points of the function. Critical points occur where the derivative of the function is zero or does not exist.
Let's find the derivative of the potential energy function:
dU/dx = d/dx (x³ - 4x² - 9x + 16)
= 3x² - 8x - 9
Now, let's find the critical points by setting the derivative equal to zero and solving for x:
3x² - 8x - 9 = 0
This is a quadratic equation. We can solve it using factoring, completing the square, or the quadratic formula. In this case, the quadratic equation factors nicely:
(3x + 1)(x - 9) = 0
Setting each factor equal to zero and solving for x gives us two possible critical points:
3x + 1 = 0 => 3x = -1 => x = -1/3
x - 9 = 0 => x = 9
Now we have two potential critical points: x = -1/3 and x = 9.
To determine the nature of these
critical points
(stable or unstable), we can analyze the sign of the second derivative of the potential energy function.
Let's find the second derivative of U(x):
d²U/dx² = d/dx (3x² - 8x - 9)
= 6x - 8
Now, let's evaluate the second derivative at each critical point.
At x = -1/3:
d²U/dx² = 6(-1/3) - 8
= -2 - 8
= -10
At x = 9:
d²U/dx² = 6(9) - 8
= 54 - 8
= 46
For stable equilibria, the second derivative should be positive, indicating a minimum. For unstable equilibria, the second derivative should be negative, indicating a maximum.
At x = -1/3, the second derivative is negative (-10), indicating an unstable equilibrium.
At x = 9, the second derivative is positive (46), indicating a stable equilibrium.
Therefore, the positions of the
stable
and unstable equilibria are as follows:
Stable equilibrium: x = 9
Unstable equilibrium: x = -1/3
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Related Questions
An object of mass 3kg was released from 40m above the ground. Using the conservation of energy, determine the velocity of the object right before hitting the ground.
Answers
Answer:
v=28m/s
Explanation:
Conservation of Energy
Ei=Ef
mgh= 1/2mv^2
9.8*40*2= v^2
784= v^2
v= 28m/s
4. The kinetic energy of a boat is calculated at 52,000 J. If the boat has a mass of 39,000
kg, with what velocity is it moving?
Answers
Answer:
The kinetic energy (KE) of an object is given by the formula:
KE = (1/2)mv^2
where m is the mass of the object and v is its velocity.
Given that the boat has a kinetic energy of 52,000 J and a mass of 39,000 kg, we can rearrange the formula to solve for v:
v = sqrt(2KE/m)
Substituting the values, we get:
v = sqrt[(2 x 52000 J) / 39000 kg]
v = sqrt(104000 J / 39000 kg)
v = sqrt(2.6667 J/kg)
v = 1.632 m/s
Therefore, the boat is moving with a velocity of approximately 1.632 m/s.
I hope you will got this answer helpful and mark it as brainliest
When I got to my cabin at camp, the other campers showered me with a chorus of greetings. "I’m Alex,” the red-headed boy closest to me said. "Javier,” called the boy with the glasses sitting next to him. "Miguel,” waved the boy in the corner. He was sitting surrounded by a pile of comic books. A fourth boy, taller than the rest, walked up and shook my hand. "I’m Asher. Grab a bunk.”
Why did the author most likely use dialogue instead of description?
A.to allow the plot to progress
B. to show how the narrator felt
C. to emphasize the point of view
D.to show who the characters are
the answer is C
Answers
c
Explanation: c because you said it lol
Answer:
c
Explanation:
A3kg crate is placed at the bottom of an inclined frictionless plane making an angle 30 ° above the horizontal and pushed up by a force F - 50N parallel to the incline as shown below . If the incline is 6 m long , then the net work done on this crate when it reaches the top of the incline is equal to :
Answers
Answer: 210 J
Explanation:
Since there is no friction, coefficient of friction, μ = 0
The free body diagram is shown below
There must be a downward force due to gravity. Thus,
Net force = applied force - downward force
From the diagram,
Downward force = mgSinθ
where
m is the mass of the crate
θ is the angle between the plane and the horizontal axis
g is the acceleration due to gravity
From the information given,
m = 3
applied force = 50N
θ = 30
g = 10 m/s^2
Net force = (50 - 3 x 9.81Sin30) = 35 N
Net work = net force x distance
Given that distance = 6m,
Net work = 35 x 6
Net work = 210 J
The number of objects that have been observed to be orbiting in the kuiper belt is approximately.
Answers
The hundreds of thousands of icy bodies larger than 100 km have been observed to be orbiting in the Kuiper belt is approximately.
What is Kuiper belt?
The region beyond Neptune known as the Kuiper Belt is made up of countless stellar objects orbiting the sun. Solid methane, ice, and ammonia make up belt objects. The belt's orbit deviates from the orbital plane and can be inclined by up to 19 degrees. Scientists searched for Planet X as a possible explanation for the origin of the belt.
What is orbit?
An orbital is a region where it is possible to estimate the likelihood of finding any electron, whereas an orbit is a fixed path that electrons follow around the atom's nucleus.
The Kuiper Belt is thought to contain a trillion comets or more and hundreds of thousands of icy bodies bigger than 100 km (62 miles).
Therefore, there may be hundreds of thousands of icy bodies larger than 100 km have been observed to be orbiting in the Kuiper belt is approximately.
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How does your collected data help you to see if you meet your criteria for success
Answers
Collected data plays a crucial role in evaluating whether the criteria for success have been met. By analyzing the collected data, one can assess the progress made towards achieving the desired goals and determine if the criteria have been fulfilled.
Data provides an objective measure of performance or outcomes, allowing for an evidence-based assessment of success. It helps to quantify and track key metrics or indicators related to the criteria for success. By comparing the actual data with the predetermined benchmarks or targets, one can determine if the criteria have been met or if further improvements are required.
Data analysis also enables the identification of trends, patterns, and correlations, providing insights into the factors influencing success. It helps in identifying areas of strength and areas that need improvement. Additionally, data can be used for comparative analysis, benchmarking against previous periods or similar projects, to gain a broader perspective on success.
In summary, collected data provides an objective basis for evaluating progress and success by comparing actual performance against predetermined criteria, identifying areas of improvement, and gaining insights for future decision-making.
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Write a 5-8 sentence summary on Earthquakes.
Answers
Answer:
An earthquake is a sudden shaking movement of the surface of the earth. It is known as a quake, tremblor or tremor. Earthquakes can range in size from those that are so weak that they cannot be felt to those violent enough to toss people around and destroy whole cities. ... An earthquake is measured on Richter's scale.
PLEASE MARK ME BRAINLIEST, PLEASEwhy is physics to study the heat absorbed by the ocean
Answers
Answer:
Heat is a source of energy
Explanation:
Just took the test
A projectile is fired into the air at a 35o angle to the horizontal and an initial velocity of 120 m/s. what are the x and y components of the velocity vector?
Answers
Answer:
See below
Explanation:
X component = 120 * cos 35° = 98.298 m/s
Y component = 120 * sin 35° = 68.829 m/s
Any object launched into space with only gravity acting on it is referred to as a projectile. Gravity is the main force affecting a projectile. The x and y components of the velocity vector are 98.298 m/s and 68.829 m/s.
When a particle is thrown obliquely close to the Earth's surface, it travels along a curving route while experiencing constant acceleration. Always pointing in the direction of the Earth's center is this curving path. Such a particle's motion is referred to as projectile motion, and its trajectory is known as the projectile's trajectory.
The components of the projectile are:
X component = 120 × cos 35° = 98.298 m/s
Y component = 120 × sin 35° = 68.829 m/s
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A light ray of wavelength 589 nm (produced by a sodium lamp) traveling through air strikes a
smooth, flat slab of crown glass at an angle of 30.0° to the normal.Find the angle of refraction, θr .
Answers
The angle of refraction for the light ray with the wavelength of 589nm traveling through air strikes a crown glass at 30.0° incidence is 19.2°.
What is refraction?Refraction is the quantity used to measure the amount of refraction taking place at any boundary when light passes between the two mediums.
Refractive index can be calculated using Snell's law, the formula for calculating angle of refraction is as follows:
n₁/n₂ = sinФ₁/sinФ₂
n₁. sin(i) = n₂. sin(r)
where, n₁ = refractive index of medium 1
n₂ = refractive index of medium 2
i = angle of incidence in air
r = angle of refraction in glass
Therefore, by putting the values in this formula we can get the angle of refraction.
(1) × sin(30°)=(1.52) × sin(r)
sin(r)= 1/2 × 1.52
sin(r) = 1/ 3.04
r = sin⁻¹(0.328)
r = 19.2°
Therefore, Angle of refraction = 19.2°
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Your question is incomplete, most probably the complete question is:
A light ray of wavelength 589 nm (produced by a sodium lamp) traveling through air strikes a smooth, flat slab of crown glass at an angle of 30.0 to the normal. If the index of refraction of the crown glass is 1.52 and the index of refraction of air is 1. Find the angle of refraction.
Which is not a reason why the mass of an atom is expressed in atomic mass units rather than in grams?
Scientists could not agree on a standard.
Atomic mass allows for mass differences in isotopes.
The mass in grams is too small to be useful.
Atomic mass units make it easier to compare the masses of atoms.
Answers
Answer:
A. scientists could not agree
Answer:
scientists could not agree on a standard
In the absence of air resistance, why does the horizontal component of velocity for a projectile such as a
bullet remain constant while the vertical component changes?
Answers
Explanation:
The vertical velocity changes because gravity is what brings the ball downwards, since gravity is what cause acclereation in free fall, acclereatiin will make the velocity become more negative.
There is no force happening on the ball in the horinzontal direction so according to Newton 1st law, the ball will remain in constant velocity n the horinzotnal direction.
after a laser beam passes through two thin parallel slits, the first completely dark fringes occur at ±17.0 ∘ with the original direction of the beam, as viewed on a screen far from the slits.
Answers
When a laser beam passes through two thin parallel slits, it creates a pattern of light and dark fringes. The first completely dark fringes occur at ±17.0° with the original direction of the beam. This phenomenon is due to the interference of the light waves from the two slits.
When a laser beam passes through two thin parallel slits, it creates a pattern of light and dark fringes on a screen placed far from the slits.
The dark fringes occur at specific angles with respect to the original direction of the beam. In this case, the first completely dark fringes occur at ±17.0°.
To understand why this happens, we need to consider the phenomenon of interference.
When light passes through the two slits, it diffracts and spreads out, creating two coherent sources of light waves.
These waves then interfere with each other, either constructively or destructively, depending on the path difference between them.
At certain angles, the path difference between the waves from the two slits is such that they interfere destructively, resulting in a dark fringe. The angle at which the first dark fringe occurs can be determined using the formula:
d * sin(θ) = m * λ
where d is the distance between the slits, θ is the angle with respect to the original direction of the beam, m is the order of the fringe (which is 1 for the first dark fringe), and λ is the wavelength of the laser beam.
In this case, the first dark fringes occur at ±17.0°. To find the wavelength of the laser beam, we need to know the distance between the slits (d) and the order of the fringe (m), which is 1. With this information, we can rearrange the formula to solve for λ:
λ = d * sin(θ) / m
However, since we don't have the values for d and m in this question, we cannot determine the exact wavelength of the laser beam. Therefore, we cannot provide a proper conclusion or answer that is more than 100 words.
In summary, when a laser beam passes through two thin parallel slits, it creates a pattern of light and dark fringes. The first completely dark fringes occur at ±17.0° with the original direction of the beam. This phenomenon is due to the interference of the light waves from the two slits. The exact wavelength of the laser beam cannot be determined without additional information.
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a train is moving at a constant velocity of 100 mph in a straight line. inside the train, there is a mechanical claw that is holding a ball. the mechanical claw is fixed and rigid and so it does not move as a result of vibrations. furthermore, the claw is located halfway along the ceiling between the front and the rear ends of the car. at one point, the ball is released. please ignore air resistance. there is no wind inside the car. the ball will fall:
Answers
The ball will fall straight down to the floor of the train.
Since the train is moving at a constant velocity in a straight line, the ball, like any other object inside the train, is also moving at the same constant velocity. When the ball is released from the mechanical claw, it will continue to move forward with the same velocity as the train. However, since there are no external forces acting on the ball, it will fall straight down due to the force of gravity, as if the train were at rest.
From the perspective of an observer outside the train, the ball would appear to follow a curved path due to the combination of its horizontal velocity (which matches that of the train) and its vertical velocity (which is due to gravity). But from the perspective of an observer inside the train, the ball appears to fall straight down, as if the train were stationary. This is because the observer inside the train is also moving at the same constant velocity as the train and the ball, and therefore has no way to detect the train's motion relative to the outside world.
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A plane flying into a headwind travels 2000 miles in 5 hours. The return flight along the same route with a tailwind takes 4 hours. Find the wind speed and the plane's speed.
Answers
The plane's speed is 450 miles per hour, and the wind speed is 50 miles per hour. This is determined by solving the equations derived from the distances and times of the flight with and against the wind.
Let's assume the speed of the plane (without considering the wind) is P, and the speed of the wind is W.
When flying into a headwind, the effective speed of the plane is reduced by the wind speed. So the equation for the outbound flight is:
P - W = 2000 miles / 5 hours
P - W = 400 miles per hour (mph) ---(Equation 1)
When flying with a tailwind, the effective speed of the plane is increased by the wind speed. So the equation for the return flight is:
P + W = 2000 miles / 4 hours
P + W = 500 miles per hour (mph) ---(Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) with two variables (P and W). We can solve this system to find the values of P and W.
Adding Equation 1 and Equation 2 together, we eliminate the variable W:
(P - W) + (P + W) = 400 mph + 500 mph
2P = 900 mph
P = 450 mph
Substituting the value of P back into Equation 1 or Equation 2, we can solve for W:
450 mph - W = 400 mph
W = 450 mph - 400 mph
W = 50 mph
Therefore, the plane's speed is 450 mph and the wind speed is 50 mph.
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help would be nice
A
B
C
D
Answers
As the projectile moves from Q to R, the magnitude of the vertical velocity increases.
option A is the correct answer.
What is vertical velocity?
The vertical velocity of a projectile is the upward velocity of the projectile.
During the upward motion of a projectile, its vertical velocity decreases as the projectile moves upwards and eventually becomes zero as the projectile reaches the maximum height.
As the projectile begins to move downwards, the vertical velocity begins to increase and eventually becomes maximum before the projectile hits the ground.
Thus, vertical velocity of a projectile increases as the projectile moves downwards.
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A high way is built using concrete slabs 12m long at 20°C.How wide should the expansion gaps between the slabs be,at 20°C,inorder to prevent the buckling of the road if the range of temperatures experienced in this particular are between 10°C and 30°C.
Answers
Given,
The length of the slab, L=12 m
The initial temperature, T₁=10°C
The final temperature, T₂=30°C
The coefficient of the linear expansion of the concrete is α=12×10⁻⁶ /°C
The change in the length of the slab is given by,
\(\Delta L=\alpha L\times\Delta T\)Where ΔT is the change in the temperature.
Therefore,
\(\Delta L=\alpha L\times(T_2-T_1)\)On substituting the known values,
\(\begin{gathered} \Delta L=12\times10^{-6}\times12\times(30-10) \\ =2.88\times10^{-3}\text{ m} \\ \approx0.003\text{ m} \end{gathered}\)Thus the expansion in the length of the slab in the given temperature range is 0.003 m.
Thus the gap between the slabs should be 0.003 m
long nonconducting cylinder (radius = 12 cm) has a charge of uniform density (5.0 nC/m3) distributed throughout its volume. Determine the magnitude of the electric field 15 cm from the axis of the cylinder.
Answers
Answer:
the magnitude of the electric field = 27.1058 V/m
≈ 27 V/m
Explanation:
given
R(radius enclosed) = 12 cm = 0.12 m
ρ(charge density) = 5.0 nC/m³ = 5.0 × 10⁻⁹C/m³
r(radius from the axis) = 15 cm = 0.15 m
using Gauss law, which states that the electric flux through any closed surface is directly proportional to the total electric charge enclosed by this surface.
attached is the calculation of the question, using Gauss law of electrostatics
During a physics experiment, helium gas is cooled to a temperature of 19.0K at a pressure of 6.00�10?2atm . What are (a) the mean free path in the gas, (b) the rms speed of the atoms, and (c) the average energy per atom?
Answers
The mean free path in the gas is given by the formula: mean free path = (k * T) / (sqrt(2) * pi * d^2 * P), where k is Boltzmann's constant, T is the temperature in Kelvin, d is the diameter of a helium atom.
P is the pressure in atm. The diameter of a helium atom is approximately 2.4 Ångstroms.
The rms speed of the atoms is given by the formula: rms speed = sqrt((3 * k * T) / (m)), where k is Boltzmann's constant, T is the temperature in Kelvin, and m is the mass of a helium atom.
The average energy per atom is given by the formula: average energy per atom = (3/2) * k * T, where k is Boltzmann's constant and T is the temperature in Kelvin.
The mean free path is the average distance an atom travels between collisions. It depends on the temperature, pressure, and size of the atoms.
The rms speed is the square root of the average of the squared speeds of the atoms. It gives an indication of the magnitude of the velocities of the atoms.
The average energy per atom is the average kinetic energy of the atoms in the gas. It depends only on the temperature and is proportional to the absolute temperature.
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Which statement best explains why the atomic theory developed efficiently?
A- scientists ignored all previous knowledge about atoms.
B- scientists had used creativity and The scientific method in their investigations.
C- scientists had used the philosophical viewpoint as a method of investigation.
D- scientists rarely repeated experiments to make sure the results were correct.
Answers
Answer:
I think its B but if not then its D
Explanation:
Answer:
b
Explanation:
3. Since Aspeon is not expected togrow, Emily believes that the following equations can be used in the valuation analysis: (1) S=[EBIT−kd(D)](1−ks)
(2) V=S+D
(3) P=(V−D0)/n0
(4) n1=n0−D/P
(5) VL=VU+TD
Answers
The equations mentioned by Emily in the valuation analysis for Aspeon are as follows:
1) Equation (1): This equation represents the value of equity (S) and calculates it based on the EBIT (earnings before interest and taxes), the tax shield provided by debt (D), and the required return on debt (kd) and equity (ks). It implies that the value of equity is equal to the adjusted EBIT after deducting the tax shield from debt.
2) Equation (2): This equation calculates the total enterprise value (V) by adding the value of equity (S) and debt (D). It represents the total worth of the company, considering both equity and debt.
3) Equation (3): This equation calculates the price per share (P) by dividing the total enterprise value (V) minus the initial debt (D0) by the number of shares (n0). It represents the price per share based on the valuation of the company.
4) Equation (4): This equation calculates the new number of shares (n1) by subtracting the dividend (D) from the initial number of shares (n0) divided by the price per share (P). It represents the adjusted number of shares after the payment of dividends.
5) Equation (5): This equation calculates the levered value (VL) by adding the unlevered value (VU) with the tax shield value (TD). It represents the value of the company after considering the tax advantages of debt.
These equations provide a framework for valuation analysis, considering factors such as earnings, taxes, debt, and equity. They help assess the value and financial implications of Aspeon's growth prospects.
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In going from one city to another, a car whose driver tends to get lost goes 30km North, 50km west, and 20km southeast Approximately how far apart are the cities?
Answers
ANSWER:
39.21 km
STEP-BY-STEP EXPLANATION:
To determine the answer we track each move just like this:
Coordinates at the start (city A): (0, 0)
Coordinates after going 30 km north: (0, 30)
Coordinates after going 50 km west: (-50, 30)
Southeast is a move down and to the right of 45°, so we calculate at each coordinate, like this:
\(\begin{gathered} d_e=20\cdot\cos45\degree=10\sqrt{2} \\ \\ d_s=20\cdot\sin45\operatorname{\degree}=10\sqrt{2} \\ \\ \text{ Therefore:} \\ \\ x=-50+10\sqrt{2}=-35.86 \\ \\ y=30-10\sqrt{2}=15.86 \\ \\ \text{ Coordinates at the start \lparen city B\rparen: \lparen-35.86, 15.86\rparen} \end{gathered}\)We calculate the distance between both points as follows:
\(\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ \text{ we replacing} \\ \\ d=\sqrt{\left(-35.86-0\right)^2+\left(15.86-0\right)^2} \\ \\ d=\sqrt{1285.9396+251.5396}=\sqrt{1537.4792} \\ \\ d=39.21\text{ km} \end{gathered}\)The distance between both cities is 39.21 km
Define gravitational force in your own words.
Answers
Answer:
The force of attraction between any two bodies due to their masses is known as gravitational force..
Help fast
Who is often referred to as the "father of modern physics?"
Rutherford
Edison
Newton
Dalton
Answers
Answer:
C. Newton
Explanation:
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A resistance is added in parallel to a 470 Ω resistance to give an effective resistance of 330 Ω. What is the approximate value of the added resistance?
Answers
The approximate value of the added resistance is 1566.67 Ω.
Let's call the value of the added resistance R. When a resistance is added in parallel, the equivalent resistance is given by:
1/Req = 1/R1 + 1/R2
where Req is the equivalent resistance, R1 is the original resistance, and R2 is the added resistance.
In this case, we know that the original resistance is 470 Ω and the equivalent resistance is 330 Ω. We can plug these values into the formula and solve for the added resistance:
1/Req = 1/R1 + 1/R2
1/330 = 1/470 + 1/R
R = 1566.67 Ω (rounded to two decimal places)
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Definition: The energy transferred by a force to a moving object.
Answers
Answer:
Force applied
Explanation:
An object will remain at its state of rest unless a non zero for act on it
Is this statement correct that all charged particles experience same force in uniform electric field
Answers
Answer:
No the statement is incorrect.
Explanation:
Mathematically, force F experience of a charge particle of magnitude q in an uniform electric field E is given as
F = E/q
In uniform electric field is where the intensity of electric field remains same throughout. However, from the above equation it is clear that force experience by the charge particle also depends upon the magnitude of charge particle as well. So, with change in charge particles the force experienced by it also changes.
Why does a solar nebula flatten into a disk instead of a sphere, even though the gravity of a nebula pulls in all directions?
A This flattening occurs because the initial shape of the nebula is already somewhat flat.
B This flattening is a natural consequence of collisions between particles in a spinning cloud.
C. This flattening occurs because of gravitational influences of nearby stars.
D. This flattening occurs because the temperature of the solar nebula decreased as it collapsed.
Answers
Solar nebula flattening is a natural consequence of collisions between particles in a spinning cloud. therefore, option B is correct.
When a solar nebula collapses under its own gravity, it begins to spin due to the conservation of angular momentum. As the cloud spins, particles within it collide and interact. These collisions cause the cloud to flatten into a disk shape rather than remaining spherical.
Angular momentum plays a crucial role in this process. The initial slight asymmetry or irregularity in the nebula's shape leads to variations in the speeds and directions of the particles' motions. As particles collide and transfer momentum, their motion tends to align along the rotational axis of the cloud, promoting the formation of a flattened disk structure.
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1. if a wave traveling through air decreases its wavelength by half, what happens to the wave speed and frequency?
Answers
Wave speed decreases by half while the frequency remains constant.
For any wave the equation \(v = f \lambda\) holds true.The frequency is a quality of a given wave and it does not change with the external parameters.So, the possibility is for the \(v\) and \(\lambda\) to change accordingly.Therefore, \(v\) and \(\lambda\) are directly proportional to each other. Thus when the wavelength decreases by half the speed also decreases by half.This can be shown as follows as well.
\(\begin{aligned}\\\small v_1 &=\small f.\lambda_1\quad\cdots\cdots(1)\\\\\small v_2 &=\small f.\frac{\lambda_1}{2}\quad\cdots\cdots(2)\\\\(2)\div&(1)\\\\\small v_2 &=\small \frac{v_1}{2}\end{aligned}\)
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the tape in a videotape cassette has a total length 281 m and can play for 2 h. As the tape starts to play, the full reel has an outer radius of 45 mm and an inner radius of 12 mm. At some point during the play, both reels will have the same angular speed?
what is this common angular speed?
Answers
The common angular speed is 6.5 x 10^⁻⁴ rad/s
What is the angular speed about?To calculate the common angular speed of the reels during play, we need to first determine the linear speed of the tape on the outer reel. We can use the formula:
Linear speed = tape length / play time
So the linear speed of the tape on the outer reel is:
Linear speed = 281 m / (2 h * 3600 s/h)
= 0.078 m/s
Then we can use the formula for linear speed to find the angular speed:
Linear speed = angular speed x radius
So the angular speed of the outer reel is:
Angular speed = Linear speed / radius
= 0.078 m/s / (45 mm / 1000 m/mm)
= 1.7 x 10^⁻⁴ rad/s
The inner reel radius is 12mm, so the angular speed of the inner reel is:
Angular speed = Linear speed / radius
= 0.078 m/s / (12 mm / 1000 m/mm)
= 6.5 x 10^⁻⁴ rad/s
This is the common angular speed of the reels when both have the same angular speed.
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