Derive an expression for the rotational inertia of the disk about the pivot. Pivot Pivul Figure > Figure Mech 3, A uniform disk of mass M and radius R is suspended vertically from pivot on its edge s0 that it is free t0 swing without friction, as shown in Figure above The disk is raised tO an initial angular displacement % with respect (0 the vertical, as shown in Figure 2 above. and released from rest The rotational inertia of the disk about its center of mass is MR? /2 . Express all algebraic answers in terms of the given quantities and fundamental constants. aS appropriale. (4) Derive an expression for the rotational inettia of the disk about the pivot

Kepler's third law, p^2 is a^3, means that the square of the total time period of a planet's revolution the sun is directly proportional to the cube of its mean distance from the Sun.

The orbits of planets around the Sun are described by Kepler's laws of planetary motion, which he published between 1609 and 1619.

A planet's orbit is an ellipse with the sun at one of its foci. Equal areas are covered by the position vector r(t) from the sun to the planet in an equal amount of time. The semi-major axis of an orbital planet's semi-major period of revolution around the sun is proportional to the cube of that semi-major period's length.

They were essential in the discovery of dark matter in the Milky Way and have been used to forecast the orbits of several objects, including comets and asteroids.

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The force between the wires is 1*10⁻⁷T.

What is ampere?

The rate at which electrons flow or current flows across an electrical conductor is measured in amperes. An electrical charge of one coulomb (6.24 x 1018 charge carriers) per second that passes a particular place is represented by one ampere of current.

What is force?

A mass-containing object's change in velocity is referred to as a force when a push or pull is applied to it. A body can change its state of rest or motion when an external force acts on it. It is directed and has a magnitude.

The concepts required to solve the given problem is magnetic field due to a current carrying wire and force on a current carrying wire due to magnetic field.

Initially, determine the magnetic field at one wire due to other wire by using expression magnetic field due to a current carrying wire. Then, determine the force on the wire by using magnetic field, length of the wire and current in the wire.

The current carrying wire creates a magnetic field around the wire and the direction of magnetic field around the wire is known by using right hand rule.

The magnitude of magnetic field B due to a current carrying wire at distance r from the wire is given by following expression.

B=Here, I is the current, and μ₀ I/2πr

Here, I is the current, and

μ₀is the permeability.

The magnetic force F on a current carrying wire is given by following expression.

F= BIL

Here, L is the length of the wire.

Step: 1

The magnitude of magnetic field B due to a current carrying wire at distance r from the wire is given by following expression.

B= μ₀ I/2πr

Substitute 1.0 A for I, 2.0 for r, and

4πr*10⁻⁷ H/m

for  μ₀ in the above equation.

B= (4πr*10⁻⁷ H/m) (1.0A)/2πr(2.0m)

=1*10⁻⁷T

Explanation:

The direction of magnetic force on each wire is depends on the direction of current in the each wire. If the current direction of current is same in both wires then force is attractive and repulsive if the direction of current is opposite in both wires.

Therefore,  force between the wires is 1*10⁻⁷T.

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Different units of pressure is:  Pascal, dyne/cm²,  pounds per square inch.

The physical force applied to an object is referred to as pressure. Per unit area, a perpendicular force is delivered to the surface of the objects. F/A is the fundamental formula for pressure (Force per unit area). Pascals are a unit of pressure (Pa). Absolute, atmospheric, differential, and gauge pressures are different types of pressure.

Hence, Pressure = Force/area.

Atmospheric pressure is measured in atm, bar, millimeters of mercury or inches of mercury (used to measure blood pressure), torr, MSW, and FSW, as well as centimeters of water.

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when there is friction, Fs=784 An object's kinetic friction coefficient with the surface it is sliding along is 0. 10. 8.0 kg make up the object's weight.

The static friction that prevents the box from moving on its own must be overcome with an adequate opposing force for the box to move. The force that opposes the relative displacement of surfaces once they are moving is known as kinetic friction, sometimes known as dynamic friction.

w = mg = (12 kg)(9.8 m/s²)

w = 117.6 N

The weight force is equal to 117.6 N, and since the normal force is equal to the weight force, we can say that the normal force is also equal to 117.6 N.

Now that we have the normal force, we can plug it into the formula for the force of kinetic friction:

fₖ = μₖ * n  

fₖ = (0.6) * (117.6)

fₖ = 70.56 N

The four basic types of friction are fluid friction, rolling friction, sliding friction, and static friction. Normal force and friction are exactly proportional to the surfaces in contact; they are independent of hardness of the touching surface.

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The formula for preventing a collision is involved recognize the hazard, Understanding the defense, and at last Act correctly, in time.

The formula for preventing a collision is called RUA, where R stands for  Recognize the hazard, Constantly check the street ahead of you, and check your mirrors. Think almost what may happen as distant in progress as possible. Never assume that an unsafe condition will have passed before you reach it. U stands for understanding the defense, There are particular ways to handle most hazardous situations on the street. When you anticipate a danger, you're able to review the circumstance in your mind and visualize your defense so that when the time comes, you are able to act rapidly sufficient to avoid an accident. The arrangement is key and the last A stands for Act correctly, Once you see the risk and choose a defense, act promptly. Never assume that the condition will clear up. The sooner you act the more time you may avoid an accident.

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Here are 3 alkali metals with physical and chemical similarity.

What is alkali metals?

Alkali metals are come from the fact that when these metals or their oxides dissolved in water.a basic solution results.

Three alkali metals -

1- hydrogen(H)

2-lithium(Li)

3-potassium(K)

Physical and chemical similarity of hydrogen -

-it is colourless and tasteless in nature.

-it is a combustible gas but not a supporter of combustion.

Physical and chemical similarity of lithium -

-it have a melting point of 180.54

-it is the lightest of all metals,with a density approximately half that of water.

Physical and chemical similarity of pottasium -

- this metal is soft and white with a silver lustre.

-it imparts a lavender colour to a flame, and it's vapour is green.

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A log weighing 890 lb is lifted by a pair of tongs as shown the forces exerted at E and F on tong DEF are 703.695 lb.

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The correct answer is : Option E : total mechanical energy

Any location (in our case, the x location) as a function of time, with the following two components, can be used to express simple harmonic motion: Amplitude: The distance between the motion's center and either extreme. Period: The length of time it takes for a motion to complete one cycle.

The greatest deviation from the mean position is the amplitude of oscillation for a body that oscillates. It is the distance between the peak or trough of the wave and its mean position. The loudness of a sound will increase with increasing sound wave amplitude.

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The five elements of sensible fiction: Fiction tales have a tendency to take region in the present or recent beyond.

Characters are involved in events that might manifest. Characters stay in places that would be or are actual.

The characters seem like real people with real troubles solved in a realistic manner. practical fiction creates imaginary characters and conditions that depict our international society.

To define four important tale factors: person, putting, plot, and topic. Literary elements are the foundational constructing blocks of all testimonies. students will discover ways to perceive six simple elements (placing, point of view, plot, man or woman, conflict, subject matter), and assess and examine whether a creator has used them.

A literary element refers to additives of a literary painting (individual, putting, plot, topic, body, exposition, finishing/denouement, motif, titling, narrative factor of view). these are technical phrases for the “what” of a work. Literary elements consist of plot, battle, character, putting, a factor of view, and topic. they are essential due to the fact they provide a framework for the author to tell their tale. They supply the reader with a manner to comply with the story and apprehend what's going on.

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The wavelength of the light is 663nm.

What is double slit interference pattern?

The wave effectively separates into two new waves that each expand out from one of the slits as it travels through both openings. Then, there is interference between these two waves. The interference pattern is made up of alternate bright and dark lines; the bright lines are referred to as fringes. The wavelength in a double-slit experiment can be calculated using the following equation:

λ [tex]= yd / D[/tex]

where,

λ = wavelength of light source

D = distance between the screen and the slit

d = slit separation

Given,  

[tex]y = 0.550 mm, d = 2.05 mm, D = 1.70m[/tex]

Subsituting the values in equation:

λ [tex]= yd / D[/tex]

λ = [tex](0.550* 10^{-3} )(2.05* 10^{-3}) / 1.70[/tex]

λ [tex]= 663nm[/tex]

The wavelength of the light is 663nm.

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The young's modulus is E = 1.4938211 × [tex]10^5 N/m^2[/tex]

The length of the rope is, L = 65 m.

The diameter of the rope is, d = 1.2 cm = 0.012 m.

The mass of climber is, m = 80 kg.

Given elongation of rope = Δ L = 1.4 m

Young's Modulus of Material is the product of the ratio of stress to strain produced in a material. Then,

E  = σ /ε

E = W / A / L/ ΔL

E = ( mg × Δ L ) ÷ (π/4 × d² ×L )

On substituting the values we get ;

( take g = 9.8 m/s^2)

E = 1097.6 / 0.0073476

E = 149,382.11 [tex]N/m^2[/tex]

E = 1.4938211 × [tex]10^5 N/m^2[/tex]

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Answer:

200 meters

Explanation:

We are given that the speed is the object is 20 m/s and we are asked to solve for the distance it goes in 10 seconds.

To do this we will use rate X time = distance

The rate = speed = 20 m/s

The time = 10 s

(20 m/s)x(10s)= 200 meters

Upon unit analysis we can see that our answer is in meters, and distance is indeed in meters, helping us know our answer is correct.

Microwaves have a wavelength between 1millimeter to 1 meter

Microwave is a form of electromagnetic radiation with wavelengths ranging from about one millimeter to one meter. Microwaves have the longest wavelength among the electromagnetic wave. Since velocity of electromagnetic wave is 3×10⁸ and it's given as frequency×wavelength.

This shows that the higher the wavelength , the lower the frequency of an electromagnetic wave and vice versa.

Therefore microwaves have very low frequency compared to other wave in electromagnetic wave like x-ray and gamma ray.

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Because infrared radiation has longer waves than red light, it has a lower frequency and contains less energy. While ultraviolet radiation has shorter wavelengths than blue or violet light, it moves up and down faster and delivers more energy per photon than visible light. In other words, they are differ in wavelength (λ).

Longer wavelengths than visible light allow infrared waves to penetrate through thick areas of gas and dust in space with less scattering and absorption. Thus, infrared radiation can reveal objects in the cosmos that optical telescopes cannot view in visible light.

On the otherside, the wavelength (λ) of UV light is shorter than the wavelength of visible light. Purple and violet light have shorter wavelengths than other colors of light, and ultraviolet light has even shorter wavelengths than violet; thus, ultraviolet light is "purpler-than-purple" or "beyond violet."

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The rotational kinetic energy of the earth is given by K = 1/2Iω²

I = rotational inertia of earth = 2MR²/5

where

M = mass of earth = 5.972 1× 0²⁴ kg

R = radius of earth = 6.4 × 10⁶ m.

ω = angular speed of earth = 2π/T

T = period of earth = 24 hours = 24 × 60 ×  60 = 86400 s = 8.64 × 10⁴ s

So, K = 1/2Iω²  

K = 1/2 × 2MR²/5 × (2π/T)²  

K = 4π²MR²/5T²  

Substituting the values of the variables into the equation, we can find the energy

K = 4π²MR²/5T²

K = 4π² × 5.972 × 10²⁴ kg × (6.4 × 10⁶ m)²/[5(8.64 × 10⁴ s)²]  

K = 4π² × 5.972 × 10²⁴ kg × 40.96 × 10¹² m²/[5(74.6496 × 10⁸ s)²]  

K = 4π² × 244.61312 × 10³⁶ kgm²/373.248 × 10⁸ s²  

K = 9656.93890286 × 10³⁶ kgm²/373.248 × 10⁸ s²  

K = 25.87 × 10²⁸ kgm²/s²

K = 2.587 × 10²⁹ J

Therefore, the rotational kinetic energy of the earth is 2.587 × 10²⁹ J

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Answer:

Wavelength = 1074 nm

Explanation:

Given:

T = 2700 K

b = 2.9·10⁻³ m·K - Wine's constant

___________

λm - ?

Wine Law:

λm =  b / T

λm =  2.9·10⁻³ / 2700 ≈ 1074·10⁻⁹ m     or  λm = 1074 nm

The erosive power increases as the velocity increases of the stream.

Power is the rate of job completion or energy delivery in science and engineering. It is denoted by the symbol W/t, which is the product of the amount of labor (W) or energy (E) transported divided by the amount of time (t).

Any given amount of work can be finished fast with a high-powered motor or slowly with a low-powered motor. Units of power, which measure work (or energy) per unit of time, include joules per second (or watts), ergs per second, and foot-pounds per minute.

For picking up material as opposed to carrying it in suspension, more velocity is required. The rate of erosion and velocity both rise during the peak discharge. Deposition and transportation are barely separated. It follows that merely a slight drop in velocity causes sedimentation.

Therefore, the erosive power decreases as the velocity increases of the stream.

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The erosive power of a stream as velocity increases because no force of interaction between positive and neutral object.

Coulomb's law states that the electric force is directly proportional to the product of the charged objects.

The electric force is also inversely proportional to the square of the distance between the charges and is denoted below:

F= kq1q2/ r² (Newton)

where,

F=electric force

k=Coulomb constant

q1, q2=charges

r=distance of separation

So, here we know that when two objects are charged and placed at some distance "d" apart then the two objects will either attract or repel each other.

If the charges are of similar type then the two objects will repel while if the charges are of opposite nature then two objects will attract each other.

So here when a charge object is near the neutral then there is NO force between two objects.

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The distance formula is given by:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

We want to find the distance between (a,b) and (x,y).

The center of the habitat is missing in the question.

Assuming the center is (a,b) where a and b are real numbers, then we can use the distance formula to obtain:

d = √[(x - a)² + (y - b)²]

For instance if the center of your habitat us (2,-1), then

d = √[(x - 2)² + (y + 1)²]

Therefore, the equation of line with distance formula can be written as

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

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Like classical novae , X-ray bursters suddenly brighten when accreted material hits the surface of the compact object and undergoes runaway nuclear fusion.

A Nova is a transient astronomical event that causes the sudden appearance of a bright, apparently "new" star (hence the name "Nova", which is a Latin word means "new") that slowly fades over weeks or months. Classical nova eruptions are the most common type. They are likely created in a close binary star system. Classical novae are the result of a hydrogen, thermonuclear runaway on top of an accreting white dwarf, in a close binary system (cataclysmic variable). Classical nova explosion are the 3rd most violent explosions than can occur in a galaxy.

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The frequency of radio waves with a wavelength of 500 m is 6 x 10⁶ Hz.

An example of electromagnetic radiation is radio waves. The wavelength of a radio wave is substantially greater than that of visible light. Radio waves are widely used by people for communication. Both rectangular and circular antennas are used by this radio tower to send and receive radio frequency energy. y.

As we know,

Speed of light = Frequency × wavelength

Speed of light (c) =  3×10⁸ m/s

Frequency(f) = ?

Wavelength (λ) = 500m

Therefore,

c = f × λ

3×10 ⁸ = f × 500

f = 3×10 ⁸ /500

f =  6 x 10⁶ Hz.

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The x-component of the total momentum of the system at time t can be expressed as [tex]m_{1} v_{1} (t)+ m_{2} v_{2} (t)[/tex] in terms of m1 , m2 , v1(t) , and v2(t) .

The momentum of the body is represented as the product of its mass and velocity;

p= m×v

Where, m is the mass of a particle and v is its velocity

The momentum of the whole system is the vector sum of individual momentum of all the particles, which can be represented as

[tex]p_{net}[/tex]=[tex]p_{1}[/tex] + [tex]p_{2}[/tex] + [tex]p_{3}[/tex] +...

The X-component of the momentum of the system is:

[tex]p_{net}[/tex] (x) = [tex]m_{1} v_{1}[/tex](t)+ [tex]m_{2} v_{2}[/tex](t)

Hence, the total momentum of the system of particles will be [tex]m_{1} v_{1} (t)+ m_{2} v_{2} (t)[/tex].

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The device that determines a cable break or short exists is Time domain reflectometer.

What is a Time domain reflectometer?

The location of defects in transmission lines and coaxial cables can be found using a Time Domain Reflectometer (TDR). The TDR scans the transmission line with a low-voltage pulsed signal to look for any impedance-related reflections. No reflections will occur if there is no impedance mismatch over the entire length of the line, but if the transmission line is interrupted at a specific location, portion of the pulsed signal will be reflected back to the TDR. The TDR can pinpoint the precise position of a problem and determine its type, such as an open circuit, short circuit, or impedance mismatch, by monitoring the timing and propagation velocity of the received pulse.

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The net force is the total of all the forces acting on an object, according to its definition. Mass can be accelerated by net force. Whether a body is at rest or in motion, another force is at work on it.

According to the formula below, the amount of net force acting on an object is equal to the object's mass times its acceleration. An object is not accelerating and is said to be in an equilibrium state if there is zero net force acting on it. The net force, also known as the total force, is the vector sum of all the forces acting on an object. This total force takes into account the fact that a force is a vector and that two forces with equal magnitudes acting in opposing directions will cancel one another out. The net force equals mass times acceleration, and the acceleration moves in the same direction as the net force. The net force and the acceleration are directly proportional.

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Answer:

9.81 m/s   ( or 32.2 ft/s )

Explanation:

At ONE second your velocity

 v = at     = 9.81 * 1 = 9.81 m/s

A child exerts a tangential 58.5 N force on the rim of a disk-shaped merry-go-round with a radius of 2.99 m. mass of the rim is 1565 kg.

Tangential force may be defined as the force which acts on a moving body in the direction of the tangent to the curved path of the body. If the velocity of the object is positive, then the acceleration will be negative. Σ F = m a the equation shows how an unbalanced force must be acting to cause negative acceleration or deceleration.

torque = force×perpendicular distance

torque=moment of inertia×angular acc

{mr²/2 }× {0.1250÷5}=2.99×58.5

on solving this eqn we get mass as 1565kg

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The balloon's negative charge draws the paper to it.

A portion of the paper near the balloon becomes positive when you place the balloon close to a small piece of paper because the negative balloon repels the electrons in the paper. The paper moves in the direction of the balloon because positive and negative forces are attracted to one another. The paper is drawn to the balloon's negative charge.

This phenomena is called charging of body by induction because the charges are being induced in this process.

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The sum of magnitude of u + v is 15.99.

Given that, magnitude of u is 5

Magnitude of v is 11

The angle between them is 40°

Let us represent u and v in vector form,

u = 5 ( cos 40° i + sin 40° j ) = 3.83 i + 3.21 j

v = 11 ( cos 40° i + sin 40° j ) = 8.42 i + 7.07 j

The sum of two vectors is given by u + v = 3.83 i + 3.21 j +  8.42 i + 7.07 j = 12.25 i + 10.28 j

Magnitude of u + v = √(12.25²+10.28²) = √( 150.063 + 105.678) = 15.99

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The heat energy present in the interior of the earth is called geothermal energy.

Hence, the heat energy present in the interior of the Earth is called geothermal energy.

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The new velocity is < 2 , 15 , 0 >.

What is velocity?
The rate at which an object's position changes in relation to a reference frame and time is what is meant by velocity. Although it may sound complicated, velocity is simply the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) as well as direction. Its SI equivalent is the metre per second (ms-1). A body is said to be accelerating if the magnitude or direction of its velocity changes.

Impulse, P = F * t
= < 10, 0, 0 >*0.3
= < 3 , 0 , 0 >
So, change in velocity, v f - v i = P / m
So, v f - < 0 , 15 , 0 > = < 3, 0 , 0 >/1.5 = < 2 , 0 , 0 >
So, v f = < 2 , 15 , 0 >

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For the best driving conditions, a speed restriction is established, and motorists are not permitted to go beyond it. A minimum speed restriction informs drivers that they are not allowed to travel any slower than the indicated speed.

The pace at which an object's location changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar number since it just has a direction and no magnitude.

It refers to how quickly an object is traveling. Speed is defined as distance traveled divided by time. m/sec is the speed measurement unit. Speed is a scalar number that represents the size of the velocity vector.

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