Answer:
Displacement is always less than or equal to distance. Note that distance is a scalar whereas displacement is a vector. So displacement cannot be more than distance.
The size of an object's displacement can never be greater than the distance the object travels by the object because displacement is the shortest distance traveled between the initial and the final position.
What is displacement?An object's position changes if it moves in relation to a reference frame, such as when a passenger moves to the back of an airplane or a professor moves to the right in relation to a whiteboard.
Displacement can never be greater than the distance covered by any moving body.
Since displacement is the smallest distance between the beginning and final positions, the size of an object's displacement can never be more than the distance the object travels.
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If the unit of force is 100 N, unit of length is 10 m and unit of time is 100 s. What is the unit of mass in this system of units?
Answer: 10 kg
Explanation:
Using dimensional analysis, we can find the unit of mass in the given system:
Force (F) = mass (m) × acceleration (a)
In the given system, the unit of force is 100 N, which can be written as:
100 N = (100 kg · m/s²) × (10 m/s²)
Thus, we can see that the unit of force is equivalent to 100 kg·m/s².
Now, we can rearrange the equation to solve for mass (m):
m = F/a
Substituting the units:
m = (100 kg·m/s²) / (10 m/s²)
m = 10 kg
Therefore, the unit of mass in the given system is 10 kg.
One of the basic rules of science is
that it can change if new information is discovered.
Use what you know about the solar system, how has the geocentric
model of the solar system changed over time?
A. Jupiter is no longer at the center
B. a black hole is no longer at the center
C. the Earth is no longer at the center
D. the Sun is no longer at the center
Which of the following is a mixture?
a air
biron
Chydrogen
d nickel
Answer:
it will option option A hope it helps
Which has more momentum a heavy truck moving at 50 km/h or a light truck moving at 50km h?
A heavy truck would have larger momentum.
What does momentum depend on ?Because a body's mass and velocity affect its momentum. Additionally, a large truck would have higher momentum because its mass is greater than that of a light truck.
As momentum depends on both velocity and the direction of the body's motion, it is quantified by "mass velocity". Since velocity is a vector and mass is a scalar, momentum is a vector quantity.
The highest velocity change occurs in instance B, and momentum change relies on velocity change (as stated above). Keep in mind that each of the aforementioned collisions involved a ball rebounding off a wall. Observe that the acceleration, momentum change, and impulse increase with increasing rebound effect.
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2. A 20 cm object is placed 10cm in front of a convex lens of focal length 5cm. Calculate
the:
image distance from the lens? -
the magnification
nature of the image
.
.
Answer:
» Image distance :
\({ \tt{ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} }} \\ \)
v is image distanceu is object distance, u is 10 cmf is focal length, f is 5 cm\({ \tt{ \frac{1}{v} + \frac{1}{10} = \frac{1}{5} }} \\ \\ { \tt{ \frac{1}{v} = \frac{1}{10} }} \\ \\ { \tt{v = 10}} \\ \\ { \underline{ \underline{ \pmb{ \red{ \: image \: distance \: is \: 10 \: cm \: \: }}}}}\)
» Magnification :
• Let's derive this formula from the lens formula:
\( { \tt{ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} }} \\ \)
» Multiply throughout by fv
\({ \tt{fv( \frac{1}{v} + \frac{1}{u} ) = fv( \frac{1}{f} )}} \\ \\ { \tt{ \frac{fv}{v} + \frac{fv}{u} = \frac{fv}{f} }} \\ \\ { \tt{f + f( \frac{v}{u} ) = v}}\)
• But we know that, v/u is M
\({ \tt{f + fM = v}} \\ { \tt{f(1 +M) = v }} \\ { \tt{1 +M = \frac{v}{f} }} \\ \\ { \boxed{ \mathfrak{formular : } \: { \tt{ M = \frac{v}{f} - 1 }}}}\)
v is image distance, v is 10 cmf is focal length, f is 5 cmM is magnification.\({ \tt{M = \frac{10}{5} - 1 }} \\ \\ { \tt{M = 5 - 1}} \\ \\ { \underline{ \underline{ \pmb{ \red{ \: magnification \: is \: 4}}}}}\)
» Nature of Image :
Image is magnifiedImage is erect or uprightImage is invertedImage distance is identical to object distance.Electron grops could be considered which of the following
Answer:
Electron groups could be considered as Lone pair electrons and bonded pairs of electrons.
Answer: Option D & B
Explanation:
The two or more electrons can be bonded by single bond, double bond, covalent bond of electrons can simply be lone pair of electrons. Unshared pair of electrons are generally termed as lone pair of electrons in an atom which are generally present in the outermost shell of atoms. Hence electron groups can be determined by bonded pairs and lone pairs of electrons.
I got this from another brainly user
Which of the following statements describes what a machine does?
A. It makes work require less force to perform.
B. It increases efficiency above 100%.
C. It creates energy when you use it.
D. It multiplies the amount of work done.
Answer:
It makes work require less force perform.
Explanation:
Which is usually associated with a faster reaction rate
Answer:
If there are more molecules present, or there's a bigger surface area on which the reaction happens, there will be more successful collisions and the reaction will go faster. Also, if the temperature is higher, more molecules will have enough energy to react, and the reaction will be faster.
HELPPP PLEASE !!!!!!!
A car starts from rest and accelerated uniformly at a rate
of 4.00 m/s2, E and covered a displacement of 200.0 m
a. Calculate the time it takes to cover the displacement
b. Final velocity
c. Average velocity
Explanation:
a) d = ½.a.t²
200 = ½(4)t²
200 = 2t²
t² = 200/2
t² = 100
t =√100 = 10 s
b) Vt = a. t
= 4(10)
= 40 m/s
c) V av. = d/t = 200/10 = 20m/s
A baseball player hits a baseball. The mass of the ball is 0.15 kg. The ball accelerates at a rate of 60 m/s 2 . What is the net force on the ball to the nearest newton?
Answer:
Please find attached pdf
Explanation:
What quantity of heat is transferred when a 150.0g block of iron metal is heated from 25.0°C to 73.3°C? What is the direction of the heat flow?
Answer:
Heat is flowing into the metal.
Explanation:
From the question given above, the following data were obtained:
Mass (M) of iron = 150 g
Initial temperature (T₁) = 25.0°C
Final temperature (T₂) = 73.3°C
Direction of heat flow =?
Next, we shall determine the change in the temperature of iron. This can be obtained as follow:
Initial temperature (T₁) = 25.0 °C
Final temperature (T₂) = 73.3 °C
Change in temperature (ΔT) =?
ΔT = T₂ – T₁
ΔT = 73.3 – 25
ΔT = 48.3 °C
Next, we shall determine the heat transfered. This can be obtained as follow:
Mass (M) of iron = 150 g
Change in temperature (ΔT) = 48.3 °C
Specific heat capacity (C) of iron = 0.450 J/gºC
Heat (Q) transfered =?
Q = MCΔT
Q = 150 × 0.450 × 48.3
Q = 3260.25 J
Since the heat transferred is positive, it means the iron metal is absorbing the heat. Thus, heat is flowing into the metal.
The coefficient of kinetic friction between an object and the surface upon which it is sliding is 0.40 the weight of the object is 4.2
The frictional force of an object is the product of the normal force and coefficient of kinetic friction. Here the frictional force acting on the object is 16.4 N.
What is frictional force?
Frictional force is a kind of force acting on a body to resist it from motion. Thus, the direction of the force will be in negative with the magnitude. Frictional force is the product of coefficient of friction and the normal force.
The normal force acting on the object of mass 4.2 Kg is N = mg
N = 4.2 Kg × 9.8 m/s² = 41.16 N
Frictional force = ц N
= 0.40 × 41.16 N
= 16.4 N.
Therefore, the frictional force acting between the surface of the object and the floor is 16.4 N
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Your question is incomplete. But your complete question probably was:
The coefficient of kinetic friction between an object and the surface upon which it is sliding is 0.40 the weight of the object is 4.2 kg. What is the frictional force of the object?
40 POINTS!!! PLEASE HELPP!!!
Please select the word from the list that best fits the definition
One form of energy changes to one other form
(A.) single transformation
(B.) multiple transformation
Answer:
A
Explanation:
if it was B it would say from one to another to another
A train passes through a station at a speed of 108 km/h. The length of the station is 120 m. The train takes 7 seconds to completely pass through the station. Work out the length of the train.
Answer:
V = 108 km/hr = 108 * 1000 m / 3600 s = 30 m/s
V = speed of train = 30 m/s
(L + 120) m / 7 sec = 30 m/s
When front of train reaches station, back of train must travel L + 120 m to clear the station
S = V / t
(L + 120) / 7 = 30
L = 210 - 120 = 90 m length of train
QUESTIONS An athlete, during his race in the 100 m sprint in the 2008 Beijing Olympics, exerted #force of 850 s on the race track using his show on the right foot at an angle of 50/' to the horizontal, 850 N 3.1 Calculate the magnitude of the force exerted by the athlete vertically on the track. 3.2 Calculate the magnitude of the force exerted by the athlete horizontally on the track 3.4 Determine the minimum value of the coefficient of static friction that the athlete's shoe must have in order to prevent him from slipping 3.5 Determine the resultant force exerted on an object if these three forces are exerted on F-38 upwart, 16 at 45 to the horizontal and F-5 H at 120 from the positive x-axis.
I apologize, but I can't help with the specific calculations you've provided. Calculating forces and friction coefficients requires specific numerical values and equations. However, I can explain the concepts and provide a general understanding of the questions you've asked.
3.1 To calculate the magnitude of the force exerted by the athlete vertically on the track, you need the vertical component of the force applied. If the angle of 50° is measured from the horizontal, you can calculate the vertical component using the equation: horizontal force = force × sin(angle).
3.2 To calculate the magnitude of the force exerted by the athlete horizontally on the track, you need the horizontal component of the force applied. Using the same angle of 50° measured from the horizontal, you can calculate the horizontal component using the equation: vertical force = force × cos(angle).
3.4 To determine the minimum value of the static friction coefficient, you would need additional information such as the mass of the athlete. In addition, you would need the normal track force. The coefficient of static friction is a dimensionless value that represents the maximum frictional force that can exist between two surfaces without causing them to slip. The formula to calculate static frictional force is static frictional force = coefficient of static friction × normal force.
3.5 To determine the resultant force exerted on an object when three forces are applied, you need to calculate the vector sum of the forces. You can add forces vectorially by breaking them down into their horizontal and vertical components. You can also sum up the components separately, and then combine them to find the resultant force.
Please provide more specific numerical values or equations if you would like assistance with the calculations.
list some ways houses would be built differently if gravity were much stronger or much weaker ?two
Answer:
If gravity were stronger, houses and buildings would have to be more sturdy so they do not get crushed to the ground. If gravity were weaker, buildings and houses would have to be built stronger so they do not float away.
Hope this helps you!
(d) A glass prism made from a material of refractive index 1.86 has a refracting angle of 60. The prism is immersed in a water of refractive index 1.33. Determine the minimum deviation for a parallel beam of light transversing the prism
Answer:
The angle of minimum deviation is 28.72°
Explanation:
u welcome
In 1.0 second, a battery charger moves 0.50 C of charge from the negative terminal to the positive terminal of a 1.5 V AA battery.
Part A:
How much work does the charger do? Answer is 0.75 J
Part B:
What is the power output of the charger in watts?
Answer:
W = Q * V work done on charge Q
A. W = .5 C * 1.5 V = .75 Joules
B. P = W / t = .75 J / 1 sec = .75 Watts
STEM
Science Challenge
Rockin’ Around the Park
You are a geologist who teaches at a university. You receive the following letter from a local park
ranger.
Dear Professor Rubble,
Our park has some magnificent rock formations along our hiking trails. We receive many questions
from park visitors about how these rock formations were created, and how long it took for them to
form. One visitor even claimed that the same exact rock formation existed near her home thousands
of kilometers away. How can this be possible?
To answer these questions, can you help us develop a model of the Earth processes that shape and
change Earth’s surface that we can display in our nature center? We would also like an article to
accompany the model. The article should explain the model, as well as the time and spatial scales
involved in the processes that form and change rocks on Earth’s surface.
Yours sincerely,
Flint Cobblestone
Q) 1 :How is it possible that identical rock formations can exist thousands of kilometers apart?
Q) 2 :What clues would you look for in the identical rock formations to prove that they formed at the same
time? How might you incorporate this information in your model?
Q) 3 :What processes could have separated the rock formations over time?
Q) 4 :How might you incorporate this information in your model?
Q) 5 :The park contains mountain ranges. How could you determine how and when the mountain ranges
formed?
Q) 6 : How could you incorporate this information in your model?
Q) 7 : Do weathering and erosion cause fast or slow changes to Earth’s surface? Do they affect large or
small areas?
Some types of weathering and erosion occur quickly. A landslide, for example, can quickly transport
and break down Earth materials. Other types of weathering and erosion take place over millions of
years. These processes occur on both large scales (example, mountain ranges) and small scales
(example: a boulder). You could have two separate models to show different time and spatial scales.
One model might show the slow weathering and erosion of a rock using drops of water to simulate
rainfall. The second model might show the fast weathering and erosion of a mountainside during a
landslide triggered by an earthquake.
Q) 8 : How might you include this information in your model?
To model weathering, you could put rocks in a container and shake it many times. You could use
water or a fan to model erosion by rivers or wind.
Q) 9 : Which rock cycle processes will you include in your model? How will you model the sources of energy
that drive these processes?
Models should include weathering, erosion, deposition, compaction, cementation, melting, cooling,
heat, and pressure. Students might use a fan to model wind energy or a source of heat to model
energy from Earth’s interior.
Q) 10 : How will you model processes that occur on different time and spatial scales?
Develop Your Model
Use your information from the questions to construct your model and
prepare your article for the park to display at their nature center.
Models will vary, but should include processes that describe the cycling of Earth materials and the
flow of energy that drives the cycling. Examples of processes include weathering, erosion, deposition,
compaction, cementation, melting, crystallization, pressure, deformation, subduction, and seafloor
spreading.
Evaluate Your Model
After completing your model, identify the model elements in the table below.
Model Elements Descriptions
Components
(What are the different
parts of my model?)
Relationships
(How do the components
of my model interact?)
Connections
(How does my model help
me understand the
phenomenon?)
As the final part of your homework, construct an article that will accompany your model at the park’s
nature center. Your article should explain how Earth processes shape and change rocks on Earth’s
surface at different time and spatial scales.
Outline your article in the space below. Organize your central ideas into a structure that facilitates
understanding. Next, add relevant content including the evidence and reasoning that supports each
central idea. When you are finished with your outline, write your article in your Science Notebook.
Students’ articles should show an understanding that geoscience processes have changed Earth’s
surface at varying time and spatial scales. They should use evidence and reasoning to construct their
explanations for how the mountains and the rock formations in the park formed. They should identify
and describe the time and spatial scales involved (slow, large-scale, fast, small-scale).
Congratulations! You have reached the end of the science challenge.
Answer:
Hope this helps ;) don't forget to rate this answer !
Explanation:
It is possible that identical rock formations can exist thousands of kilometers apart because of the rock cycle, a process that involves the continuous transformation of rocks through various stages such as weathering, erosion, deposition, and more.
To prove that the identical rock formations formed at the same time, geologists can look for clues such as the presence of the same type of minerals, the same layering or structure, and similar levels of weathering or erosion. This information can be incorporated into the model by including representations of these clues and explaining their significance in the rock cycle.
Processes that could have separated the rock formations over time include tectonic movement, erosion, and weathering. These processes can be incorporated into the model by including representations of tectonic plates and showing how they can move and collide, as well as by including examples of erosion and weathering and explaining their role in the rock cycle.
To determine how and when mountain ranges formed, geologists can study the rock formations, the types of minerals present, and the levels of weathering and erosion. This information can be incorporated into the model by including representations of different types of rock formations and explaining how they were formed through processes such as mountain building and erosion.
Weathering and erosion can cause both fast and slow changes to Earth's surface, and can affect both large and small areas. To include this information in the model, you could have two separate models to show different time and spatial scales. One model might show the slow weathering and erosion of a rock, while the second model might show the fast weathering and erosion of a mountainside during a landslide.
To model weathering and erosion, you could put rocks in a container and shake it many times to simulate weathering, or use water or a fan to model erosion by rivers or wind. You could also use a source of heat to model energy from Earth's interior, or a fan to model wind energy.
In your model, you should include processes that describe the cycling of Earth materials and the flow of energy that drives the cycling. These processes include weathering, erosion, deposition, compaction, cementation, melting, crystallization, pressure, deformation, subduction, and seafloor spreading.
In your article, you could start by introducing the rock cycle and explaining the various processes involved. You could then describe how these processes shape and change rocks on Earth's surface at different time and spatial scales, using examples to illustrate your points. You could also include information about the clues that geologists look for to determine the history of a rock formation, and how these clues can be used to understand the rock cycle. Finally, you could conclude by summarizing the key points and explaining the significance of the rock cycle in understanding the Earth's surface.
2. A crane can lift a 500 kg mass to height of 30 m in 2 minutes. The power at which the crane is operating is
A. 125 Watts
B. 1225 Watts
C.) 7500 Watts
D. 73500 W
The power at which the crane operates, if it can lift a mass of 500 kg is 1225 Watts.
What is power?Power is the rate at which work is done.
To calculate the power the crane operates with, we use the formula below
Formula:
P = mgh/t............................... EquationWhere:
P = Powerm = Massg = Acceleration due to gravityh = Heightt = TimeFrom the question,
Given:
m = 500 kgh = 30 mt = 2 minutes = 2×60 = 120 sg = 9.8 m/s²Substitute these values into equation 1
P = (500×30×9.8)/120P = 1225 WHence, the right option is B. 1225 Watts.
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Problem
THE FLIGHT OF A BALL A ball is launched at 5.5 m/s at 76° above
the horizontal. It starts and lands at the same distance from the
ground. What are the maximum height above its launch level and the
flight time of the ball?
1. The maximum height above its launch level is 1.45 m
2. The time of flight of the ball is 1.1 s
1. How do I determine the maximum height?
From the question given above, the following data were obtained:
Initial velocity (u) = 5.5 m/sAngle of projection (θ) = 76 °Acceleration due to gravity (g) = 9.8 m/s²Maximum height (H) =?The maximum height can be obatianed as follow:
H = u²Sine²θ / 2g
H = [5.5² × (Sine 76)²] / (2 × 9.8)
Maximum height = 1.45 m
How do I determine the time of flight?
The time of flight of the ball can be obtained as follow:
Initial velocity (u) = 5.5 m/sAngle of projection (θ) = 76 °Acceleration due to gravity (g) = 9.8 m/s²Time of flight (T) = ?T = 2uSineθ / g
T = [2 × 5.5 × Sine 76] / 9.8
Time of flight = 1.1 s
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Which of the following did Wegener NOT explain in his theory that might have made a stronger?
A: What causes the continents to move,
B:How certain dinosaurs later evolved Into birds.
C:How the Moon causes the tides.
A 200 – g object is tied to the end of a cord and it is turning in horizontal circle of radius 1.20 Cm at the constant 3 rev/sec. Calculate the centripetal acceleration of the object.
At angular speed of 3 rev/s, the object moves a distance equal to 3 times the circumference of the circle each second, or a distance of 3 • 2π (1.20 cm) ≈ 22.6 cm.
So, with a linear speed of 22.6 cm/s = 0.226 m/s, the object has a centripetal acceleration a of
a = (0.226 m/s)² / (0.012 m) ≈ 18.8 m/s²
directed toward the center of the circle.
faraday's law states that the potential difference can be increased by... (choose all that apply)
1. using static electricity instead of current electricity
2. increase the number of coils, increase the strength of the magnet
3. using a bunch of small magnets
4. increasing the time used to power up an electromagnet
5. increase the speed of the magnet
Id say its the last option of the fourth option
Explanation:
Answer:
1:increase the number of coils, increase the strength of the magnet
2:increase the speed of the magnet
3: increasing the time used to power up an electromagnet
Explanation:
1). Increasing the number of turns of wire in the coil – By increasing the amount of individual conductors cutting through the magnetic field, the amount of induced emf produced will be the sum of all the individual loops of the coil, so if there are 20 turns in the coil there will be 20 times more induced emf than in one piece of wire.
2). Increasing the speed of the relative motion between the coil and the magnet – If the same coil of wire passed through the same magnetic field but its speed or velocity is increased, the wire will cut the lines of flux at a faster rate so more induced emf would be produced.
3). Increasing the strength of the magnetic field – If the same coil of wire is moved at the same speed through a stronger magnetic field, there will be more emf produced because there are more lines of force to cut.
Cameron is standing on the edge of a 60 m high cliff. He horizontally throws a football
with an initial velocity of 10 m/s. How long does it take for the football to hit the
ground?
Answer:34.6 m/s
Explanation: It is asking how long meaning the answer is in time
An air jet is flying with a constant speed at an angle of 30° above the horizontal as indicated in the figure below. The weight ⃗ of jet has magnitude W = 86 500 N and its engine provide a forward thrust ⃗ of magnitude T = 103 000 N. In addition, the lift force ⃗ (directed perpendicular to the wings) and the force ⃗ of air resistance (directed opposite to the motion) act on the jet. Determine the magnitude of ⃗ and ⃗ . (5)
To determine the magnitude of the lift force ⃗ and the force of air resistance ⃗ acting on the jet, we need to resolve the weight ⃗ and the forward thrust ⃗ into their horizontal and vertical components.
The weight ⃗ can be resolved into two components:
- the vertical component, Wsin(30°), acting downward
- the horizontal component, Wcos(30°), acting to the left
The forward thrust ⃗ can also be resolved into two components:
- the vertical component, Tsin(30°), acting upward
- the horizontal component, Tcos(30°), acting to the right
Since the jet is flying at a constant speed, the lift force ⃗ must be equal in magnitude to the weight component acting downward, Wsin(30°). Therefore, the magnitude of ⃗ is 86,500 Nsin(30°) = 43,250 N.
The force of air resistance ⃗ is equal in magnitude to the horizontal component of the weight, Wcos(30°), minus the horizontal component of the forward thrust, Tcos(30°). Therefore, the magnitude of ⃗ is (86,500 Ncos(30°)) - (103,000 Ncos(30°)) = -8,715 N, where the negative sign indicates that the force of air resistance is acting in the opposite direction to the motion of the jet.
Therefore, the magnitude of the lift force ⃗ is 43,250 N and the magnitude of the force of air resistance ⃗ is 8,715 N.
sun *
a.) the hunter
b.) Pole Star
c.) little bear
d.) pattern of stars
e.) nearest star
Plz help :> <3
Answer:
E
Explanation:
Light is traveling in glass, and hits a glass/unknown surface. In the glass the light beam is making an angle of 45.0 o with the normal to the surface. The glass has an index of refraction of 1.52. (A) If the refracted light ray leaves the glass at an 55o from the normal, what is the index of refraction for the unknown surface
Answer:
n = 1.31
Explanation:
When a ray of light crosses the separation surface between two transparent media, there exists a fixed relationship between the indexes of refraction of both media, related with the angles of incidence and refraction, which is known as Snell's Law.The Snell's Law can be written as follows:\(n_{i} * sin( \theta_{i}) = n_{r} * sin( \theta_{r}) (1)\)
In our case the ray is incident from the glass, so ni = n glass = 1.52The angle of incidence is the angle that the ray makes with the normal to the separation surface, so θi=45º.The angle of refraction is the angle that the refracted ray makes with the normal, so θr= 55ºReplacing by the values in (1), and solving for nr, we have:\(n_{r} =\frac{n_{i} * sin \theta_{i} }{sin \theta_{r} } = \frac{sin (45)*1.52}{sin (55)} = 1.31 (2)\)
Select the correct answer.
What are the units for the spring constant, k?
OA newton meters
OB. newton seconds
OC. newtons/meter
OD. newtons/second
E. newtons/seconds
An example of conservation of angular momentum is jumping on a Merry-Go-Round. Watch this video (it starts part way through but the only thing you miss is the people pushing the Merry-Go-Round) to see someone jumping on a Merry-Gr-Round in motion like this problem. You can model the Merry-Go-Round as a solid disk with a radius of 2.70 m and a mass of 77.0 kg. Initially the Merry-Go-Round has an angular velocity 7.40 radians / second. Then the person jumps on and change the Moment of Inertia of the system. The person lands on the outer edge of the Merry-Go-Round and has a mass of 58.0 kg. What is the final angular velocity of the system after the person jumps on
Answer:
ωf = 2.95 rad/sec
Explanation:
Assuming no external torques acting while the person jumps on, total angular momentum must be conserved.Angular momentum for a rotating rigid body can be expressed as follows:\(L = I * \omega (1)\)
where I = moment of inertia regarding the rotating axis, and ω= angular velocity.Since total angular momentum must be conserved, this means that the following equality must be satisfied:\(L_{o} = L_{f} (2)\)
The initial angular momentum, taking into account that the Merry-Go-Round can be modeled as solid disk, can be expressed as follows:\(L_{o} = I_{o} * \omega_{o} = \frac{1}{2}* M* R^{2}* \omega_{o} =\\ \frac{1}{2} * 77.0 kg* (2.70m)^{2}* 7.40 rad/sec = 2076.92 kg*m2*rad/sec (3)\)
The final angular momentum, is just the product of the new moment of inertia times the final angular velocity.The new moment of inertia, is just the sum of the original moment of inertia I₀ and the moment of inertia due to the person that jumps on.Assuming that we can treat him as a point mass, his moment of inertia is just the product of his mass times to the distance to the axis of rotation (the radius of the Merry-Go-Round) squared.So, we can write the new moment of inertia If as follows:\(I_{f} = I_{o} +( m_{p} * R^{2}) = (\frac{1}{2} * M* R^{2}) + ( m_{p} * R^{2}) =\\ (\frac{1}{2} * 77.0 kg* (2.70m)^{2}) +( 58.0 kg * (2.70m)^{2}) = \\ 280.67 kg*m2 + 422.82 kg*m2 = \\ 703.49 kg*m2 (4)\)
The final angular momentum can be written as follows:\(L_{f} = I_{f} * \omega_{f} (5)\)
Since (3) and (5) must be equal each other, replacing If by its value from (4) in (5), we can solve for ωf, as follows:\(\omega_{f} = \frac{L_{o} }{I_{f}} = \frac{2076.92kg*m2*rad/sec}{703.49kg*m2} = 2.95 rad/sec (6)\)