An early submersible craft for deep-sea exploration was raised and lowered by a cable from a ship. When the craft was stationary, the tension in the cable was 5500 N. When the craft was lowered or raised at a steady rate, the motion through the water added an 1800 N drag force.What was the tension in the cable when the craft was being lowered to the seafloor?

Answer:

[tex]1.11\times10^{-4} C[/tex]

Explanation:

Coulomb's force:

[tex]F=\frac{kqq'}{d^2}[/tex]

where, q and q' are two charges, d is the distance between them and k is the Coulomb constant.

The net force on charge q at origin is 17 N.

[tex]17 = 9\times 10^9 \times 8.5\times10^{-6}[\frac{-28\times 10^{-6}}{0.21^2}+\frac{q_2}{0.36^2}]\\17 = 76.5 \times 10^3[-6.35 \times 10^{-4}+7.72q_2]\\q_2 = 1.11\times10^{-4} C[/tex]

Answer:

5.35 x 10^-5 C

Explanation:

q1 = - 28 micro Coulomb =- 28 x 10^-6 C

q2 = ?

q3 = 8.5 micro Coulomb = 8.5 x 10^-6 C

y1 = 0.21 m

y2 = 0.36 m

q3 is at origin.

Let F1 is the force between q1 and q3 and F2 is the force between q2 and q3.

By use of Coulomb's law, the force between the two charges is given by

[tex]F = \frac{Kqq'}{r^{2}}[/tex]

Now, [tex]F_{1} = \frac{Kq_{1}q_{3}}{0.2^{2}}[/tex]

[tex]F_{1} = \frac{9\times 10^{9}\times 28\times 10^{-6}\times 8.5\times 10^{-6}}{0.21^{2}}[/tex]

F1 = 48.6 N    .... (1)

Now, [tex]F_{2} = \frac{Kq_{2}\times q_{3}}{0.36^{2}}[/tex]

[tex]F_{2} = \frac{9\times 10^{9}\times q_{2} \times 8.5\times 10^{-6}}{0.36^{2}}[/tex]

F2 = 590277.78 q2   .... (2)

Now, F1 - F2 = 17

48.6 - 590277.78 q2 = 17     from (1) and (2)

q2 = 5.35 x 10^-5 C

Thus, the charge on q2 is 5.35 x 10^-5 C.  

Answer:

greater than 0.10

Explanation:

The null hypothesis is:

[tex]H_{0} = 10.2[/tex]

The alternate hypotesis is:

[tex]H_{1} > 10.2[/tex]

Our test statistic is:

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the statistic, [tex]\mu[/tex] is the mean, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

We have that:

[tex]t = 0.45[/tex]

We are testing if X is greater than 0.45, so our pvalue is 1 subtracted by the pvalue of z = t = 0.45.

z = 0.45 has a pvalue of 0.6736

1 - 0.6735 = 0.3264

So our pvalue is 0.3264, which is greater than 0.10.

So the correct answer is:

greater than 0.10

Here the test sta-tis-tics should be greater than 0.10.

Since In 1990s, the average amount of time spent playing computer games was 10.2 hours per week.

Here, t = 0.45

So in the case when X is greater than 0.45, so our pvalue is 1 subtracted by the p-value of z = t = 0.45.

z = 0.45 has a p-value of 0.6736

1 - 0.6735 = 0.3264

Now

our p-value is 0.3264, which is greater than 0.10.

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Answer:D

Explanation:

Answer:

d.

Explanation:

Answer:

Black color absorbs heat more quickly and it also emits heat at a faster rate.

Whereas silver is one of the best conductor of heat and electricity. Therefore, it absorbs heat more quickly but it does not emit heat at a faster rate.

Therefore, we can conclude that the statement black pot emits heat at a faster rate than the silver pot best explains that black pot is significantly cooler than the water in the silver pot.

Explanation:

Hope this helps :)

Final answer:

The black pot cools faster than the silver pot because black emits infrared radiation more efficiently, thereby losing heat quicker.

Explanation:

The difference in the temperature of the water in the two identical pots, one black and the other silver, after being heated and left to cool in the same room, can be explained by the properties of radiative heat transfer. Darker colors, especially black, are known to radiate heat more efficiently than lighter colors. This means that the black pot will emit more infrared radiation than the silver pot and thus cool down faster. Both pots start at the same temperature, and given identical conditions aside from color, the differing cooling rates are due to how effectively each color emits heat as radiation.

Answer:

The heater use 583 kWh of electrical energy per month.

Explanation:

Given that,

Power of the water heater, P = 550 watts

It is operated for 106 hours

The electrical energy used by the heater per unit time is called its power. So,

[tex]P=\dfrac{E}{t}\\\\E=P\times t\\\\E=5500\ W\times 106\ h\\\\E=583000\ Wh\\\\E=583\ kWh[/tex]

So, the heater use 583 kWh of electrical energy per month.

Answer:

i think its true

Explanation:

Polarization is the non-symmetrical distribution of charges within a neutral object, and it does not mean that the object becomes charged.

The statement, "When an object becomes polarized, it acquires a charge and becomes a charged object," is false. Polarization is the separation of positive and negative charges within an inherently neutral object. For example, consider two metallic spheres that are neutral. When a charged glass rod is approached to the spheres, it induces a negative charge on the side nearest to the rod, leaving the other side of the spheres positively charged. However, the spheres as a whole remain electrically neutral. This is an instance of induced polarization.

It's also crucial to understand that charging by polarization does not require direct contact with a charged object. When the spheres are separated before the charged rod is removed, each sphere will have a net charge, which is the result of charging by induction, not by transfer of charge through contact. This process can be repeated multiple times without depleting the excess charge on the rod, emphasizing the non-contact nature of the process.

Answer:

Potential energy is converted into kinetic energy by a force. For example, when you pick up a rock, you work against gravity to give it some potential energy. And then when you drop it, the gravitational force causes the rock to accelerate towards the ground

Explanation:

Potential energy is transformed into kinetic energy through various natural processes. An example is a rollercoaster which at the peak has high potential energy due to its height, but as it descends and increases speed, the potential energy is transformed into kinetic energy. This phenomenon is guided by the Law of Conservation of Energy.

In physics, potential energy is stored energy that an object has due to its position or state. Kinetic energy on the other hand, is the energy that an object possesses due to its motion. The transformation between these two forms of energy occurs continuously in the natural world.

For instance, think of a rollercoaster at the peak of a track. It has a high potential energy because of its height. As the rollercoaster starts to descend, the potential energy is transformed into kinetic energy as the rollercoaster increases speed (due to gravity). When it gets to the lowest point, all of its potential energy has been converted into kinetic energy. This cycle continues for the duration of the ride, with the rollercoaster's energy constantly being transformed between potential and kinetic.

This transformation between potential and kinetic energy is referred to as the Law of Conservation of Energy, which states that energy cannot be created or destroyed, it can only be transformed from one form to another.

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Answer:

[tex]5.868 \times 10^7 Pa[/tex]

Explanation:

If half the gas is drawn then pressure would have dropped by half

[tex]P_1 = 10^8 /2 = 5\times10^7 Pa[/tex]

Assuming ideal gas, if temperature rises from 15c (T1 = 15 + 273 = 288 K) to 65 c (T2 = 65 + 273 = 338 K), then we have the following equation for ideal gas

[tex]\frac{P_1}{T_1} = \frac{P_2}{T_2}[/tex]

[tex]P_2 = T_2\frac{P_1}{T_1} = 338\frac{5\times10^7}{288} = 5.868 \times 10^7 Pa[/tex]

Answer:

The magnetic flux through the two cubes is zero in both cases

Explanation:

To answer this question, we have to think about the nature of magnetic fields.

In fact, we know that magnetic sources always exist only as magnetic dipoles: this means that a magnet always has a north pole (from which the magnetic field lines go away) and a south pole (into which the magnetic field lines return). There exist no magnetic monopoles: even when we cut a magnet in a half, we end up having two magnets, each of them having its own north pole and south pole.

A direct consequence of this fact is that if we take a closed surface, such as a cube surrounding the magnet, the magnetic flux through the cube is always zero. This is because all the field lines going out the surface of the cube always return inside the cube on another point. Since the magnetic flux basically represents the number of field lines passing through the surface of the cube, this means that the net positive magnetic flux (lines going out of the cube) is equal to the net negative magnetic flux (lines going into the cube).

As a result, the magnetic flux is zero for both the smaller cube and the larger cube.

Answer:

7.33 rounded

Explanation:

Speed = distance divided time

S = d/t

Suppose a Rollerblade racer finished a 132 meter race in 18 seconds. What is the average speed of the Rollerblade racer?

S = 132 divided 18

Speed = 7.33 rounded

Answer: 7.3 meters a second

Explanation: 132/18=7.3

Answer:

a) [tex]k = 200.016\,\frac{N}{m}[/tex], b) [tex]m = 1.389\,kg[/tex], c) [tex]f = 0.524\,hz[/tex]

Explanation:

a) The maximum speed of the oscillating block-spring system is:

[tex]v_{max} = \omega \cdot A[/tex]

The angular frequency is:

[tex]\omega = \frac{v_{max}}{A}[/tex]

[tex]\omega = \frac{1.2\,\frac{m}{s} }{0.1\,m}[/tex]

[tex]\omega = 12\,\frac{rad}{s}[/tex]

The mass of the system is:

[tex]E = \frac{1}{2}\cdot m\cdot v_{max}^{2}[/tex]

[tex]m = \frac{2\cdot E}{v_{max}^{2}}[/tex]

[tex]m = \frac{2\cdot (1\,J)}{(1.2\,\frac{m}{s} )^{2}}[/tex]

[tex]m = 1.389\,kg[/tex]

The spring constant is:

[tex]\omega = \sqrt{\frac{k}{m} }[/tex]

[tex]k = \omega^{2}\cdot m[/tex]

[tex]k = (12\,\frac{rad}{s} )^{2}\cdot (1.389\,kg)[/tex]

[tex]k = 200.016\,\frac{N}{m}[/tex]

b) The mass is:

[tex]m = 1.389\,kg[/tex]

c) The frequency of oscillation is:

[tex]\omega = 2\pi\cdot f[/tex]

[tex]f = \frac{2\pi}{\omega}[/tex]

[tex]f = \frac{2\pi}{12\,\frac{rad}{s} }[/tex]

[tex]f = 0.524\,hz[/tex]

Answer:

a) F = 20 N

b) m = 1.39 kg

c) f = 1.909 Hz

Explanation:

Given

E = 1 J

A = 0.1 m

vmax = 1.2 m/s

a) F = ?

b) m = ?

c) f = ?

Solution

a) We apply the equation

E = 0.5*k*A²

then

k = 2*E/A²

k = 2*1 J/(0.1 m)²

k = 200 N/m

then we use the equation

F = kA

F = (200 N/m)(0.1 m)

F = 20 N

b) We use the formula

E = K + U

if U = 0 J

then

E = K = 0.5*m*v²

⇒  m = 2*K/v²

m = 2*1 J/(1.2 m/s)²

m = 1.39 kg

c) we apply the equation

f = (1/2π)√(k/m)

then

f = (1/2π)√(200 N/m/1.39 kg)

f = 1.909 Hz

Answer:

Increases

Explanation:

Since power P=IV

Then it means when current increases, the power increases hence brightness increases. I represent current, P is power and v is voltage.

Current of capacitor when in series connection is given by

[tex]I=2\pi fCV[/tex]

where I is current across capacitor, f is frequency, C is capacitance and v is voltage across capacitance. From this second formula, it is evident that an increase in capacitance increases the current across the capacitor. Therefore, if current increases, power also increases leading to an increase in brightness

Increasing the capacitance in a series circuit with an AC source and a light bulb generally increases the bulb's brightness because it reduces the capacitive reactance and allows more current to flow through the bulb. So, the correct option is A.

When an AC source is connected to a series combination of a light bulb and a variable capacitor, the brightness of the bulb is affected by the capacitive reactance of the circuit, which is inversely proportional to both the frequency of the AC source and the capacitance of the capacitor.

As the capacitance is increased (considering the frequency of the AC source is constant), the capacitive reactance decreases. This allows more current to flow through the bulb, which generally increases the bulb's brightness.

Since capacitors in an AC circuit cause the current to lead the voltage, an increase in capacitance will mean that the current increases while the voltage across the capacitor does not change significantly. Therefore, the energy dissipated by the light bulb in the form of light (and heat) increases.

Answer:the fields are at right angles to each other and to the direction of the wave.

Explanation: gradpoint

Answer:

-5.8 m/s

Explanation:

Given:-

- The mass of Big Bubba, mb = 125 kg

- The mass of Lil' Pete, mp = 80 kg

- The initial velocity of Big Bubba, vb = 7 m/s

- The initial velocity of Lil Pete , vp = -10 m/s

- The velocity after impact of Lil' Pete, vp' = + 10 m/s

- The velocity after impact of Big Bubba = vb'

Find:-

what is  Big Bubba's velocity after the collision?

Solution:-

- We will consider the two football players as particles of mass mb and mp with their respective velocities vb and vp heading towards each other.

- The masses collide and both reverse in direction with velocities vb' and vp'.

- The system of the two masses have no external forces acting on it; hence, the system is isolated from any fictitious forces.

- For above conditions we can apply the principle of conservation of linear momentum. The linear momentum of two football players before ( Pi ) and after the impact ( Pf ) remain constant. The conservation is:

                             Pi = Pf

           mb*vb + mp*vp = mb*vb' + mp*vp'

           mb*vb + mp*( vp - vp' ) = mb*vb'

- Develop an expression for Big Bubba's velocity after impact vb':

           vb' = vb + mp/mb*( vp - vp' )

- Plug in the values and evaluate:

         vb' = 7 + 80/125*( -10 - 10 )

         vb' = 7 - 80*20 / 125

          vb' = -5.8 m/s  

Answer: The velocity of Big Bubba after impact is vb' = -5.8 m/s

Answer:

Relative dating involves the dating of geological events and

formations that occured/existed throughout the whole geological

history, and this eventually gives the relative age of the earth.

While, Absolute dating involves the use of isotopes and radioactive

elements (radioactivity) and also the study and relation of

meteorites and moon rocks, which eventually gives the   actual/absolute age of the earth. The meteorites and moon rocks are

believed to have formed virtually at the same time with earth and

are therefore, considered to be of the same age as earth.

Explanation:

Answer:

Absolute dating and relative dating are both methods used to determine the age of a fossil. Absolute dating gives the actual age of a fossil in years based on the amount of radioactive and stable elements in the fossil. Relative dating gives an estimate of the age of a fossil based on the location of the fossil in relation to other fossils.  

Explanation:

sample response

Answer:yes it isss

Explanation:

Answer:

Steam-methane reforming

Electrolysis of water

Explanation:

Steam methane reforming involves reaction of methane with water in the presence of a catalyst such as nickel to form Carbon oxides and Hydrogen.

CH4 + H2O ⇌ CO + 3 H

Electrolysis of water involves splitting of water through application of electric current to give Hydrogen and Oxygen gas.

2 H2O(l) → 2 H2(g) + O2(g)

Hydrogen gas for fuel cells is commonly produced through steam reforming and electrolysis. In steam reforming, steam is passed over coke to produce hydrogen and carbon monoxide. In electrolysis, water is split into hydrogen and oxygen gases with a power supply.

The two most common ways to produce hydrogen gas used in fuel cells are through steam reforming and electrolysis. Steam reforming involves passing steam over coke at high temperatures, which produces a mixture of carbon monoxide and hydrogen gas, also known as water gas.

In the electrolysis process, water is split into hydrogen and oxygen gases by the addition of energy using a battery or power supply. For fuel cells, hydrogen obtained from these processes is continuously fed into the cell with an oxidant and undergoes redox chemistry that generates electrical energy and water as the waste product. The fuel cell reactions are catalyzed on graphite electrodes embedded with platinum-based catalysts.

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Answer:

Explanation:

Lightning is seen before the thunder is heard because , velocity of light exceeds velocity of sound. We also know that velocity , wavelength and frequency are related as follows

velocity = frequency x wavelength

velocity of light > velocity of sound

frequency of light x wavelength of light > frequency of sound x wavelength of sound

But given wavelength of light = wavelength of sound

Putting this relation in the equation above

frequency of light x wavelength of light > frequency of sound x wavelength of light

cancelling out equal terms on both sides

frequency of light  > frequency of sound

frequency of light will be greater than frequency of sound.

Answer:

the frequency of thunder is more than the frequency of lightning

Explanation:

Light waves (lightning) are faster than sound waves (thunder). If their wavelengths are the same, then the frequency of light waves must be larger

Answer:

Length,  Area, Conductivity, Temperature

Explanation:

The factors affection the resistance of a conductor are

(1) Length of the conductor (L): As the length (L) of the conductor increases, the Resistance(R) of the conductor also increase.

R ∝ L

(2) Cross sectional Area of the conductor(A): As the cross sectional area of the conductor(A) increases, the Resistance (R) of the of the conductor decreases.

R ∝1/A

(3)  conductivity of the conductor(G): As the conductivity of the (G) of the conductor increases, the Resistance(R) of the conductor decreases.

R ∝ 1/G

(4) Temperature(T): As temperature(T) increases, the Resistance(R) of a conductor decreases.

T ∝ R

Answer:

Explanation:

There are four factors affecting resistance which are

Temperature,

Length of wire,

Area of the cross-section of wire and

nature of the material.

You really can't tell.

Power = I^2 × R = V^2 / R ( unit in Watt)

For P = I^2 × R

Where we have P directly proportional to R, increase in Power leads to increase in R

So if we have 100 will have higher resistance

For P = V^2/R

Power is inversely proportional to resistance.

So increase in Power leads to decrease in resistance.

60 watt will have a higher resistance.

Answer:

4. C, B, D, A

Explanation:

This is a simple experiment to make electromagnets. Electromagnets are the instrument/object which behave like magnet when electricity is passed around them. As long as electricity is supplied they will behave like magnet. When the electricity is stopped, they will no longer behave like magnet.

The correct sequence, as per the question, to make electromagnet are listed below:

Wrap a wire to create loops around a piece of metal, such as iron. (As of now it will not behave like magnet)

As soon as we close the circuit, current starts flowing through the loops and generate magnetic field.

This magnetic field forces the magnetic domains inside metal piece to align  and the metal starts behaving like a magnet.

Answer:

Red Dwarf

Explanation:

Answer:10 hz

Explanation

A wave has a speed of 30 m/s and a wavelength of 3 meters then its frequency is 10 Hz.

Wave is is a disturbance in a medium that carries energy as well as momentum . wave is characterized by amplitude, wavelength and phase. Amplitude is the greatest distance that the particles are vibrating. especially a sound or radio wave, moves up and down. Amplitude is a measure of loudness of a sound wave. More amplitude means more loud is the sound wave.

Wavelength is the distance between two points on the wave which are in same phase. Phase is the position of a wave at a point at time t on a waveform.

There are two types of the wave longitudinal wave and transverse wave.

Longitudinal wave : in which, vibration of the medium (particle) is parallel to propagation of the wave. Sound wave is a longitudinal wave.

Transverse wave : in which, vibration of the medium (particle) is perpendicular to propagation of the wave. Light wave is a transverse wave.

Frequency of the wave is given by,

f = c/λ

f = 30/3 = 10 Hz

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Using Hooke's Law, we determined the spring constant to be approximately 1230 N/m. For a 3.3 kg mass, the extension is 2.63 cm. Therefore, the total length of the spring is 9.63 cm.

To find the length of the spring when a 3.3 kg mass is suspended from it, we need to determine the spring’s force constant (k). Using Hooke's Law, F = kx, where F is the force due to the mass, k is the spring constant, and x is the extension. First, convert the masses to forces (F = mg) using g = 9.8 m/s².

Now, we use this constant to find the extension for the 3.3 kg mass:

Add the extension to the original spring length:

New length of the spring: 7 cm + 2.63 cm = 9.63 cm.

Answer:

[tex]\Delta h = 5.212\,m[/tex]

Explanation:

The inelastic collision is modelled by using the Principle of Momentum Conservation:

[tex](3.8\,kg)\cdot (19\,\frac{m}{s} ) + (1.6\,kg)\cdot (-11\,\frac{m}{s} ) = (3.8\,kg + 1.6\,kg)\cdot v[/tex]

The final velocity is:

[tex]v = 10.111\,\frac{m}{s}[/tex]

The maximum height of the composite system is:

[tex](0\,\frac{m}{s})^{2} = (10.111\,\frac{m}{s} )^{2} - 2\cdot (9.807\,\frac{m}{s^{2}} )\cdot \Delta h[/tex]

[tex]\Delta h = 5.212\,m[/tex]

Answer:

5.21m

Explanation:

We are given that;

mass of first ball; m1 = 3.8kg

Speed of first ball; v1 = 19 m/s upwards

Mass of second ball; v2 = 1.6 kg

Speed of second ball; v2 = 11 m/s downwards

From conservation of linear momentum,

m1v1 + m2v2 = m_t•v_t

Where,

m1v1 is momentum of first ball

m2v2 is momentum of second ball

m_t•v_t is the combined momentum of the 2 balls.

Let's make v_t the subject

v_t = [m1v1 + m2v2]/m_t

m_t is the combined mass of both balls.

Since first and second ball are moving in opposite directions, thus;

v_t = [m1v1 - m2v2]/m_t

Thus, m_t = 3.8 + 1.6 = 5.4kg

Thus, plugging in the relevant values, we have;

v_t = [(3.8 x 19) - (1.6 x 11)]/5.4

v_t = [(3.8 x 19) - (1.6 x 11)]/5.4

v_t = (72.2 - 17.6)/5.4

v_t = 54.6/5.4 = 10.11 m/s

Now, from equation of motion,

v² = u² + 2gh

Where u is initial velocity which is now v_t while final velocity v is zero.

Now, since gravity is acting against motion, g = - 9.8m/s²

Thus,

v² = u² + 2gh gives;

0² = 10.11² - (2 x 9.8 x h)

19.6h = 102.212

h = 102.212/19.6

h = 5.21 m

Answer:

[tex]-\frac{F_2}{m_1}[/tex]

Explanation:

First of all, we notice that the collision is elastic: this means that there are no external forces acting on the system, as the total momentum and the total kinetic energy of the system are conserved.

The force acting on the cart 2 is

[tex]F_2[/tex]

According to Newton's third law of motion:

"When an object 1 exerts a force on another object 2, then object 2 exerts an equal and opposite force on object 1"

Therefore, if we call [tex]F_1[/tex] the force exerted on cart 1 during the collision, we can write

[tex]F_1=-F_2[/tex]

According to Newton's second law of motion, the net force acting on an object is equal to the product between its mass (m) and its acceleration (a):

[tex]F=ma[/tex]

So for cart 1 we have:

[tex]F_1=m_1 a_1[/tex]

And som the acceleration of cart 1 is

[tex]a_1=\frac{F_1}{m_1}=-\frac{F_2}{m_1}[/tex]

Where the negative sign means that the direction of the acceleration of cart 1 is opposite to the direction of the force F2.

Answer:

An example of kinetic energy due to gravity can be a ball held in the air (Kinetic energy is energy an object has because of it's motion.).

Explanation:

Answer: to win the game by at least two points. If the score reaches 20–20, then 21 points are no longer enough to win the game. You need to win two clear points: two points in a row, one after the other. For example, 22–20 would be a winning score, as would 25–23.

Explanation:    you need a lot of points to be won

your welcome

In badminton, a game is won by a player or team reaching a specific number of points first with a 2-point lead.

Badminton is a racquet sport played either as singles or doubles, with the objective of hitting a shuttlecock over a net to the opponent's side. It requires agility, speed, and hand-eye coordination and is popular for recreational play and competitive tournaments worldwide. In badminton, a game is won by a player or team reaching a specified number of points first. In singles, the first player to reach 15 points wins, while in doubles, the first team to reach 21 points wins.

However, in order to win, a player or team must also have a lead of at least 2 points. This means that if both players or teams reach the required number of points simultaneously, the game continues until one player or team has a 2-point lead. In addition, there are specific rules regarding serving and scoring that players must follow to win a badminton game.

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Answer:

[tex]-20.0 kg m^2/s[/tex]

Explanation:

The angular momentum of an object in rotation is given by

[tex]L=I \omega[/tex]

where

I is the moment of inertia

[tex]\omega[/tex] is the angular speed

In this problem, initially we have

[tex]I=2 kg m^2[/tex] is the moment of inertia of the wheel

[tex]\omega_i = 6.0 rad/s[/tex] is the initial angular speed

So the initial angular momentum is

[tex]L_i = I\omega_i = (2)(6.0)=12 kg m^2/s[/tex]

Later, a counterclockwise torque of

[tex]\tau=-5.0 Nm[/tex] is applied

So the angular acceleration of the wheel is:

[tex]\alpha = \frac{\tau}{I}=\frac{-5.0}{2}=-2.5 rad/s^2[/tex] in the direction opposite to the initial rotation.

As a result, the final angular velocity of the wheel will be:

[tex]\omega_f = \omega_i + \alpha t[/tex]

where

t = 4.0 is the time interval

Solving,

[tex]\omega_f = +6.0 +(-2.5)(4.0)=-4 rad/s[/tex]

which means that now the wheel is rotating in the counterclockwise direction.

Therefore, the new angular momentum of the wheel is:

[tex]L_f = I\omega_f =(2)(-4.0)=-8.0 kg m^2/s[/tex]

So, the change in angular momentum is:

[tex]\Delta L=L_f - L_i = (-8.0-(12))=-20.0 kg m/s^2[/tex]