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Parallel Plate Capacitor (considering the material)

The capacitance of a two parallel plates capacitor both of area A separated by a distance d is calculated by the area of overlap of the two plates, ... more

Parallel Plate Capacitor

A capacitor is an electrical/electronic device that can store energy in the electric field between a pair of conductors. The simplest capacitor consists of ... more

Capacitance

Capacitance is the ability of a body to store an electrical charge. Any object that can be electrically charged exhibits capacitance. Capacitance is a ... more

Vacuum tube - transconductance

In electronics, a vacuum tube, an electron tube, or colloquially a tube (North America) or valve (British usage), is a device that controls electric ... more

Electric field (Uniform)

A uniform electric field is produced by placing a potential difference (or voltage) across two parallel metal plates. A uniform field is one in which the ... more

Dynamic (shear) viscosity

The dynamic (shear) viscosity of a fluid expresses its resistance to shearing flows, where adjacent layers move parallel to each other with different ... more

Townsend avalanche (Townsend discharge)

The Townsend discharge is a gas ionization process where free electrons, accelerated by a sufficiently strong electric field, give rise to electrical ... more

Shear rate

Shear rate is the rate at which a progressive shearing deformation is applied to some material. The shear rate for a fluid flowing between two parallel ... more

First Townsend ionization coefficient

The Townsend discharge is a gas ionization process where free electrons, accelerated by a sufficiently strong electric field, give rise to electrical ... more

Moment of inertia of a thin rectangular plate (Axis of rotation at the end of the plate)

Moment of inertia is the mass property of a rigid body that determines the torque needed for a desired angular acceleration about an axis of rotation. ... more

Moment of inertia of a thin rectangular plate (Axis of rotation in the center of the plate)

Mass moment of inertia measures the extent to which an object resists rotational acceleration about an axis, and is the rotational analogue to mass. Moment ... more

Capacity of coaxial cable - Cylindrical Capacitor

A capacitor is an electrical/electronic device that can store energy in the electric field between a pair of conductors. Its capacity depends on the ... more

Chladni's Law

Chladni’s law, named after Ernst Chladni, relates the frequency of modes of vibration for flat circular surfaces with fixed center as a function of ... more

Supercsapacitor - Time to deliver a Constant Power

A supercapacitor (SC) (sometimes ultracapacitor, formerly electric double-layer capacitor (EDLC)) is a high-capacity ... more

Supercsapacitor - Time to deliver a Constant Current

A supercapacitor (SC) (sometimes ultracapacitor, formerly electric double-layer capacitor (EDLC)) is a high-capacity ... more

Capacitance of Concentric spheres capacitors

Capacitance is the ability of a body to store an electrical charge. Any object that can be electrically charged exhibits capacitance. Concentric or ... more

Critical Buckling Compressive Loading of a Plate

In science, buckling is a mathematical instability that leads to a failure mode.

When a structure is subjected to compressive stress, buckling may ... more

Moment of Inertia - Rod end

Moment of inertia is the mass property of a rigid body that determines the torque needed for a desired angular acceleration about an axis of rotation. ... more

Hydraulic efficiency (pumps)

Due to leakage of fluid between the back surface of the impeller hub plate and the casing, or through other pump components – there is a volumetric ... more

Energy Density (electric field)

Lenz’s law /ˈlɛnts/ is a common way of understanding how electromagnetic circuits obey Newton’s third law and the conservation of energy. ... more

Child's Law - related to anode voltage

First proposed by Clement D. Child in 1911, Child’s law states that the space-charge limited current (SCLC) in a ... more

Capacitance of a Pair of parallel identical wires

Capacitance is the ability of a body to store an electrical charge. Any object that can be electrically charged exhibits capacitance. The capacitance is a ... more

Capacitors conected in series

Connected in series, the capacitors each store instantaneous charge build-up equal to that of every other capacitor in the series. The total voltage ... more

Stored Energy (Electrical Charge)

Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. Here we can calculate for Stored Energy ... more

Energy stored in a system of three point charges

Electric potential energy, or electrostatic potential energy, is a potential energy that results from conservative Coulomb forces and is associated with ... more

Stored Energy (Potential Difference)

Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. Here we can calculate for Stored Energy ... more

Worksheet 333

A typical small rescue helicopter, like the one in the Figure below, has four blades, each is 4.00 m long and has a mass of 50.0 kg. The blades can be approximated as thin rods that rotate about one end of an axis perpendicular to their length. The helicopter has a total loaded mass of 1000 kg. (a) Calculate the rotational kinetic energy in the blades when they rotate at 300 rpm. (b) Calculate the translational kinetic energy of the helicopter when it flies at 20.0 m/s, and compare it with the rotational energy in the blades. (c) To what height could the helicopter be raised if all of the rotational kinetic energy could be used to lift it?


The first image shows how helicopters store large amounts of rotational kinetic energy in their blades. This energy must be put into the blades before takeoff and maintained until the end of the flight. The engines do not have enough power to simultaneously provide lift and put significant rotational energy into the blades.
The second image shows a helicopter from the Auckland Westpac Rescue Helicopter Service. Over 50,000 lives have been saved since its operations beginning in 1973. Here, a water rescue operation is shown. (credit: 111 Emergency, Flickr)

Strategy

Rotational and translational kinetic energies can be calculated from their definitions. The last part of the problem relates to the idea that energy can change form, in this case from rotational kinetic energy to gravitational potential energy.

Solution for (a)

We must convert the angular velocity to radians per second and calculate the moment of inertia before we can find Er . The angular velocity ω for 1 r.p.m is

Angular velocity

and for 300 r.p.m

Multiplication

The moment of inertia of one blade will be that of a thin rod rotated about its end.

Moment of Inertia - Rod end

The total I is four times this moment of inertia, because there are four blades. Thus,

Multiplication

and so The rotational kinetic energy is

Rotational energy

Solution for (b)

Translational kinetic energy is defined as

Kinetic energy ( related to the object 's velocity )

To compare kinetic energies, we take the ratio of translational kinetic energy to rotational kinetic energy. This ratio is

Division

Solution for (c)

At the maximum height, all rotational kinetic energy will have been converted to gravitational energy. To find this height, we equate those two energies:

Potential energy

Discussion

The ratio of translational energy to rotational kinetic energy is only 0.380. This ratio tells us that most of the kinetic energy of the helicopter is in its spinning blades—something you probably would not suspect. The 53.7 m height to which the helicopter could be raised with the rotational kinetic energy is also impressive, again emphasizing the amount of rotational kinetic energy in the blades.

Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics
Creative Commons License : http://creativecommons.org/licenses/by/3.0/

Coulomb's constant

Coulomb’s constant, the electric force constant, or the electrostatic constant (denoted ke ) is a proportionality constant in equations relating ... more

Speed of light in matter

The speed of light in vacuum is the speed at which all massless particles and changes of the associated fields (including electromagnetic radiation such as ... more

Cross Section (discrete events)

The cross section is an effective area that quantifies the intrinsic likelihood of a scattering event when an incident beam strikes a target object, made ... more

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