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Energy – Momentum relation

In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating any object’s rest (intrinsic) ... more

Relativistic momentum of rigid bodies

In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a ... more

Relativistic kinetic energy of rigid bodies

In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a ... more

Mass - Energy equivalence

In physics, mass–energy equivalence states that anything having mass has an equivalent amount of energy and vice versa, with these fundamental quantities ... more

Frequency (Doppler effect for a moving black body)

Black-body radiation is the thermal electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, or emitted by ... more

Compton wavelength

The Compton wavelength is a quantum mechanical property of a particle. The Compton wavelength of a particle is equivalent to the wavelength of a photon ... more

Electromagnetic mass ( longitudinal mass) by Lorentz

Due to the self-induction effect, electrostatic energy behaves as having some sort of momentum and “apparent” electromagnetic mass, which can ... more

Electromagnetic mass (transverse mass) by Lorentz

Due to the self-induction effect, electrostatic energy behaves as having some sort of momentum and “apparent” electromagnetic mass, which can increase the ... more

Kinetic energy (related to object's momentum)

In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is the work needed to accelerate a body of a given mass ... more

Temprature of a black body

Black-body radiation is the thermal electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, or emitted by ... more

Energy Density (magnetic field)

Energy density is the amount of energy stored in a given system or region of space per unit volume or mass, though the latter is more accurately termed ... more

Larmor formula

The Larmor formula is used to calculate the total power radiated by a non relativistic point charge as it accelerates or decelerates. This is used in the ... more

Radiation Pressure by Reflection (using particle model: photons)

Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. Radiation pressure implies an interaction between ... more

Energy Density of electric and magnetic fields

Energy density is the amount of energy stored in a given system or region of space per unit volume or mass, though the latter is more accurately termed ... more

Malus' law in X-ray (relavistic form)

A polarizer or polariser is an optical filter that passes light of a specific polarization and blocks waves of other polarizations.
When a perfect ... more

Redshift (based on wavelength)

In physics, redshift happens when light or other electromagnetic radiation from an object is increased in wavelength, or shifted to the red end of the ... more

Redshift: 1+z (based on frequency)

In physics, redshift happens when light or other electromagnetic radiation from an object is increased in wavelength, or shifted to the red end of the ... more

Redshift: 1+z (based on wavelength)

In physics, redshift happens when light or other electromagnetic radiation from an object is increased in wavelength, or shifted to the red end of the ... more

Redshift (based on frequency)

In physics, redshift happens when light or other electromagnetic radiation from an object is increased in wavelength, or shifted to the red end of the ... more

Orbital Eccentricity

The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect ... more

Sagnac effect (phase difference)

The Sagnac effect, also called Sagnac interference, named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is ... more

Energy of a Photon

A photon is an elementary particle, the quantum of light and all other forms of electromagnetic radiation, and the force carrier for the electromagnetic ... more

Tsiolkovsky rocket equation - acceleration based

The Tsiolkovsky rocket equation, classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that ... more

Specific Relative Angular Momentum - Elliptical orbit

In celestial mechanics, the specific relative angular momentum (h) of two orbiting bodies is the vector product of the relative position and the relative ... more

Law of Conservation of Linear Momentum - 2 particles example

In classical mechanics, linear momentum or translational momentum (pl. momenta; SI unit kg m/s, or equivalently, N s) is the product of the mass and ... more

Sagnac Effect - TIme Difference

The Sagnac effect (also called Sagnac interference), named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is ... more

Gravitational wave - Binaries (Orbital lifetime)

Gravitational waves are disturbances in the curvature (fabric) of spacetime, generated by accelerated masses, that propagate as waves outward from their ... more

Von Mises yield criterion

The von Mises yield criterion suggests that the yielding of materials begins when the second deviatoric stress invariant reaches a critical value. The von ... more

Angular Acceleration

Torque, moment, or moment of force is the tendency of a force to rotate an object about an axis, fulcrum, or pivot.
Moment of inertia is the mass ... 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/

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