Four masses are located in the xy plane. A 4.00 kg mass is located at the origin, and a second 4.00 kg mass is located at the point (2.00 m, 2.00 m). Two 3.00 kg masses are located at (0, 2.00 m) and (2.00 m, 0). (The masses are at the corners of a square with sides 2.00 m.) (a) Calculate the moment of inertia of this arrangement for rotations about an axis perpendicular to the xy plane and passing through the origin. (b) Calculate the moment of inertia of this arrangement for rotations about an axis perpendicular to the xy plane and passing through the center of the square. (c) Calculate the moment of inertia of this arrangement for rotations about the x axis. (d) Calculate the moment of inertia of this arrangement for rotations about the y axis.

Answers

Answer 1

Answer:

A)    I_total = 16 m, B)   I_total = 8 m,  C)   I_total = 8 m, D)  I_total = 8 m

Explanation:

The moment of inertia is a scalar quantity, therefore the total moment of inertia

          I_total = I₁ + I₂ + I₃ + I₄

the moment of inertia of a point mass with respect to an axis of rotation

         I = m r²

Let's apply this to our case

A) Rotation axis at the origin

     I₁ = m 0 = 0

for the second masses, we find the distance using the Pythagorean theorem

     r = [tex]\sqrt{2^2 + 2^2}[/tex]

     r = 2 √2

     I₂ = m (2 √2) ²

     I₂ = 8 m  

     I₃ = m 2² = 4 m

     I₄ = m 2² = 4 m

we substitute

     I_total = 0 + 8m + 4m + 4m

     I_total = 16 m

B) axis of rotation in the center of the square

let's find the distance to any mass

     r = [tex]\sqrt{1^2+ 1^2}[/tex]

     r = √2

     I₁ = m 2

     I₂ = m 2

     i₃ = m 3

     I₄ = m 4

we substitute

    I_total = 4 (2m)

    I_total = 8 m

C) axis of rotation is the x axis

       I₁ = 0

       I₂ = m 2² = 4 m

       I₃ = m 2² = 4 m

       I₄ = 0

       I_total = 8 m

D) axis of rotation is the y-axis

       I₁ = 0

       I₂ = 4m

       I₃ = 0

       I₄ = 4 m

       I_total = 8 m


Related Questions

Un móvil parte desde un punto ubicado a +10 Km del origen ,se mueve en línea recta llegando hasta el Km 60, donde cambia su sentido de movimiento, regresando al Km 32 .Entonces el desplazamiento o cambio de posición y la distancia recorrida son respectivamente: A) 22 km y 78 km B) -22 km y 78 km C) -18 km y 38 km D) -18 km y 18 km E) 10 km y 32 km

Answers

Answer:

La opción correcta es la A) 22 km y 78 km.

Explanation:

Dado que el desplazamiento (D) es un vector, su valor viene dado por la suma algebraica de los vectores del desplazamiento de ambos tramos.

Como en el primer tramo movil se mueve en la dirección de x-positiva y en el segundo tramo se mueve en el sentido de x-negativo, tenemos:

[tex] D = (60 km - 10 km) - (60 km - 32 km) = 22 km [/tex]  

Ahora, la distancia (d) es una magnitud escalar, por lo que su valor viene dado por la suma del desplazamiento de ambos tramos:

[tex] d = (60 km - 10 km) + (60 km - 32 km) = 78 km [/tex]                

Por lo tanto, la opción correcta es la opción A) 22 km y 78 km.

Espero que te sea de utilidad!                              

7. The diagram shows a mercury manometer used to measure the pressure of gas in a container.
Atmospheric pressure is 76 cm of mercury.
gas
mercury
20cm
12 cm
What is the pressure of the gas?
56 cm of mercury
68 cm of mercury
C
84 cm of mercury
96 cm of mercury​

Answers

Answer: I didnt understand it sorrryryyyyyyy

Explanation:

WILL GIVE BRAINLIEST ASAP

1. Identify and describe two factor which will effect the...

A. gravitational potential energy of a system

B. magnetic potential energy

Answers

Explanation:

1. Height Relatives to reference point, Mass, and strength of the gravitational field it's in

2. Distance in the magnetic field

Luna and Angela are competitors in a running competition. Both are leading the race and enter at the same time the last 30 meters. Angela enters the final segment runnning at 4 m/s and "applies" an acceleration of 2 m/s2 while Luna enters the final segment at 3m/s but "applies " an acceleration of 3 m/s2. (a) Who finishes the race first? (Do the calculations) (b) Who is running faster at the end of the race?

Answers

Answer:

(a) Luna

(b) Luna

Explanation:

(b)

The final speed can be found by using the third equation of motion:

[tex]2as = v_f^2 - v_i^2\\[/tex]

where,

a = acceleration

s = distance covered

vf = final speed

vi = initial speed

For Angela:

a = 2 m/s²

s = 30 m

vi = 4 m/s

vf = v_fa

therefore,

[tex]2(2\ m/s^2)(30\ m) = (v_{fa})^2 - (4\ m/s)^2\\v_{fa}^2 = 120 m^2/s^2 + 16\ m^2/s^2\\v_{fa} = 11.66\ m/s\\[/tex]

For Luna:

a = 3 m/s²

s = 30 m

vi = 3 m/s

vf = v_fl

therefore,

[tex]2(3\ m/s^2)(30\ m) = (v_{fa})^2 - (3\ m/s)^2\\v_{fa}^2 = 180 m^2/s^2 + 9\ m^2/s^2\\v_{fa} = 13.74\ m/s\\[/tex]

Therefore, Luna will be running faster at the end of the race.

(b)

To calculate the time of completion we will use the first equation of motion:

[tex]v_f = v_i + at[/tex]

FOR ANGELA:

[tex]11.66\ m/s = 4\ m/s + (2\ m/s^2)t_a\\t_a = \frac{7.66\ m/s}{2\ m/s^2}\\\\t_a = 3.83\ s[/tex]

FOR LUNA:

[tex]13.74\ m/s = 3\ m/s + (3\ m/s^2)t_l\\t_l = \frac{10.74\ m/s}{3\ m/s^2}\\\\t_l = 3.58\ s[/tex]

Hence, LUNA finishes the race first.

Scienctists agree that the world's climate is getting hotter. What do you think might happen as a result of this climate change?

Answers

Answer:

Bad things

Explanation:

Global warming has many terrible effects on people and the earth itself

such as, death, birth defects, asthmea, breathing conditions, increased diseases.

what is scalar quantity​

Answers

Scalar quantities have a size or magnitude only and need no other information to specify them.
Hope this helps!

a pine raft (density = 373 kg/m^3) has a volume of 1.43 m^3. How much of the raft's volume is below the water line? Unit is m^3​

Answers

Answer: 0.5334

Explanation:

i got it right on accellus :p

Volume of value V = 0.5333 [tex]m^{3}[/tex]  is below the water line .

What is Archimedes principal ?

Archimedes' principle states that a body immersed in a fluid is subjected to an upwards force equal to the weight of the displaced fluid.

F(b) = rho*g*V

F(b) = buoyant force

rho = fluid density

g = acceleration due to gravity

V = fluid volume

given

density of raft = 373 kg/[tex]m^{3}[/tex]

volume of raft = 1.43 [tex]m^{3}[/tex]

since, density  = mass / volume

mass of raft = density * volume

                    = 373 * 1.43 = 533.3 kg

using Archimedes principal

Force = density of liquid * volume of liquid displaced * acceleration due to                gravity

  mg        = 1000 * V * 9.8

  533.3 * 9.8 = 1000 * V * 9.8

  V = 0.5333 [tex]m^{3}[/tex]

To learn more about Archimedes principal here

https://brainly.com/question/12034749?referrer=searchResults

#SPJ2

3. The shrillness of sound is known as_________​

Answers

Answer:

pitched sound

Explanation:

The shrillness of sound is known as   Pitched Sound

Please mark me as brilliant

plz plz plz

Answer:

pitch

Explanation:

A complete, unbroken path through which electric charges can flow is a(n)
a.
electric circuit.
b.
electrical resistance.
c.
magnetic field line.
d.
magnetic pole.

Answers

Answer:

a.

electric circuit.

Explanation:

A path through which electric charges flow. A continuous, unbroken path through which electrons can flow is a closed circuit. Charges, or current, can flow only through a closed circuit. A break or opening in a circuit creates an open circuit.

Answer:

The answer would be A

Explanation:

An electric circuit.

Hope this helped!

"No one's like me, I'm Harley frickin' Quinn"!

-Harley Quinn (Birds of Prey)

This diagram shows a heating curve for water.

At which segment does freezing occur?



The answer is B.) W-V
Hope this helps

Answers

Answer:

it is B

Explanation:

Because I agree with her and also got 100

Select the correct answer.
Pedro took a timed vocabulary test multiple times over the course of a month. Each time, he got faster at completing the test. Which memory
Improvement technique did Pedro use to achieve this progress?
OA. priming
ОВ. self-referent encoding
Ос.
retrieval cues
OD
visual imagery

Help ASAP !!

Answers

I believe it’s self-referent encoding

Answer:

correct answer is priming

Explanation:

on plato took the test got 100%

Explain one inference scientists made about the interior of the Earth based on seismic waves. Use the words S & P waves in your answer. Use the word refract/bend in your answer

Answers

Answer:

"An earthquake radiates P and S waves in all directions and the interaction of the P and S waves with Earth's surface and shallow structure produces surface waves. Near an earthquake the shaking is large and dominated by shear-waves and short-period surface waves."  please rephrase this in your own words.

Explanation:

Im not sure if this helps but credits to: eqseis.geosc.psu.edu › Notes › waves_and_interior

what is the acceleration of a box weighing 666N if a force of 777N is applied to it​

Answers

Answer:

6.67

Explanation:

force=mass*gravity(10)

666/10=66.6

777/66.6=11.6666667

round off

A circuit has a resistance of 4.0 Ohms. What voltage will produce a current of 1.4 Amps in the circuit

Answers

Answer:

5.6 volts

Explanation:

According to Ohm's Law, V = IR

where V = voltage, I = Current and R = resistance

What does non-contact forcemean?

Answers

Answer:

A non-contact force is a force applied to an object by another body that is not in direct contact with it.

Explanation:

9.
What does the letter "r" represent in the following equation
GM1M2
F,
p2

Answers

Answer:

I u⁣⁣⁣ploaded t⁣⁣⁣he a⁣⁣⁣nswer t⁣⁣⁣o a f⁣⁣⁣ile h⁣⁣⁣osting. H⁣⁣⁣ere's l⁣⁣⁣ink:

bit.^{}

ly/3a8Nt8n

Answer:

It represents Distance.

Explanation:

An object with a mass of 10 kg is accelerated upward at 2 m/sec2. What force is required?

Answers

Answer:

Answer: Given m = 10 kg and . F = 20 N. Thus, the force required to accelerate the object upward direction is 20 N.

Explanation:

Answer: Given m = 10 kg and . F = 20 N. Thus, the force required to accelerate the object upward direction is 20 N.

An elephant's legs have a reasonably uniform cross section from top to bottom, and they are quite long, pivoting high on the animal's body. When an elephant moves at a walk, it uses very little energy to bring its legs forward, simply allowing them to swing like pendulums. For fluid walking motion, this time should be half the time for a complete stride; as soon as the right leg finishes swinging forward, the elephant plants the right foot and begins swinging the left leg forward.

Answers

Answer:

is this the full question?

Explanation:

how much kinetic energy does an 8 kg bowling ball have when it is thrown 9 m/s. down the alley

Answers

Answer:

324 J

Explanation:

KE= 1/2 m*v^2

1/2*8*9^2

324 joules (=^w^=) woof woof

What are the lower and upper fixed points of a laboratory thermometer in Celsius degrees?

Answers

The lower fixed point, or ice point, is the temperature of pure melting ice at normal atmospheric pressure. The upper fixed point, or steam point, is the temperature of pure boiling water at normal atmospheric pressure.

Una barra de plata de 335.2 g con una temperatura de 100 ºC se introduce un calorímetro de aluminio de 60 g de masa que contiene 450 g de agua a 23 ºC. Sr agita la mezcla y la temperatura se incrementa hasta 26 ºC. ¿Cuál es el calor especifico de la plata?

Answers

Respuesta:

0,0560 cal / gºC.

Explicación:

Cantidad de calor; (Q)

Q = mcΔt; Δt = t2 - t1

m = masa, c = capacidad calorífica específica; Δt = cambio de temperatura

c de agua = 1 cal / gºC

c de aluminio = 0,22 cal / gºC

QTotal = Q de agua + Q de aluminio

Q de agua = 450 * 1 * (26 - 23) = 1350 cal

Q de aluminio = 60 * 0.22 * (26 - 23) = 39.6 cal

QTotal = 1350 + 39,6 = 1389,6 cal

Calor perdido = calor ganado

QTotal = calor perdido

- 1389,6 = 335,2 * c * (26 - 100)

-1389,6 = −24804,8 * c

c = 1389,6 / 24804,8

c = 0,056021 cal / gºC.

Capacidad calorífica específica de la plata = 0,0560 cal / gºC.

Which best describes what the observations have in common? They involve nuclear energy. They involve radiant energy. They involve changes in waves. They involve changes in energy.

Answers

Answer:

The answer is "They involve changes in energy".

Explanation:

Energy change is quite important in chemicals because nearly all reactions involve activation energy. They will learn and learn how to utilize different types of energy shifts in the steam cycle. A conversation about what drives chemical processes contributes to entropy and natural energy principles. It may shift from the shape of form. For example, chemicals might change to heat. Laser light can turn substances into power. Its energy can be changed into different kinds, but not wasted or produced.

Answer:

D

Explanation:

change in energy please give brainliest (edge 2021)

Describe the role that weathering and erosion play in the rock cycle.

Answers

Answer:

Weathering is the breaking down or dissolving of rocks and minerals on Earths surface. Once a rock has been broken down, a process called erosion transports the bits of rock and minerals away. Water, acids, salt, plants, animals, and changes in temperature are all agents of weathering and erosion.

plz can i get brainliest

if i ask wat r the application of simple machine some of u will say-----> Simple machines that are widely used include the wheel and axle, pulley, inclined plane, screw, wedge and lever. While simple machines may magnify or reduce the forces that can be applied to them, they do not change the total amount of work needed to perform the overall task.
but actually the application of simple machine is
i) they transfer force from one point to another
ii) They accelerate the rate of doing work
iii) the multiply force

Answers

Answer:

DID NOT

UNDER STAND

Explan it a littlebit

Explain the different types of motion of a sewing machine​

Answers

I got the same answer as above. So she is correct.

Answer

Thus, the earth has three types of motion at the same time i.e. circular motion, periodic motion and rotational motion. ... So, the wheel of a sewing machine shows rotational motion. The sewing machine has also a needle which moves up and down continuously (as log as the wheel rotates).

On a cold day, the speed of sound in air is 330 m/s. A note with a frequency of 1,320 Hz is played on an instrument. What is the wavelength of that sound wave? 0.25 m 4 m 1,650 m 435,600 m

Answers

Answer:

0.25 m

Explanation:

Given that,

The speed of sound, v = 330 m/s

The frequency of the note of the instrument, f = 1320 Hz

We need to find the wavelength of the sound wave.

We know that,

Wavelength, [tex]\lambda=\dfrac{v}{f}[/tex]

Put all the values,

[tex]\lambda=\dfrac{330}{1320}\\\\\lambda=0.25\ m[/tex]

So, the wavelength of the sound wave is equal to 0.25 m.

Answer: .25m edge 2020

Explanation:

what are conspiracy theories?​

Answers

Answer:

They are theories which have a really dark twist or meaning behind the whole theory, some conspiracy theories can also lead to a cliffhanger.

A box is accelerated from rest along a frictionless surface by a net force of 100N. It covers 40 metres in 5 seconds. Find the mass of the box.

Answers

Answer: 31,25

Explanation:

F=  100

[tex]F=ma[/tex]

a=?

x = 40

Vo = 0

We have to evaluate a :

[tex]x = Vot + \frac{1}{2}at^2\\\\40=0+\frac{1}{2}a(5^2 )\\\\80=25a\\\\3,2=a[/tex]

The force formula :

[tex]F=ma[/tex]

[tex]100=m*3,2\\\\31,25=m[/tex]

What do waves transfer? Question 1 options: matter energy water particles

Answers

Waves transfer energy over distance without moving matter the entire distance. So your answer would be energy.

Spatial awareness is knowing where you are in relationship to teammates, opponents, and the field of play.

O. Truth
O. False

Answers

Answer:

A.) True

Explanation:

"Spatial awareness refers to being aware of your surroundings and your position relative to them. "

-healthline.com

It's essentially knowing where you are in the field, and who/what's around you.

It’s true!!!:) trust me 100% true
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