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Flywheel energy storage (Energy density)

A flywheel is a rotating mechanical device that is used to store rotational energy. Flywheel energy storage works by accelerating a rotor to a very high ... more

Regenerative brake (KERS Flywheel energy)

A regenerative brake is an energy recovery mechanism which slows a vehicle or object by converting its kinetic energy into a form which can be either used ... more

Magnus effect

The Magnus effect is the commonly observed effect in which a spinning ball (or cylinder) curves away from its principal flight path.The overall behaviour ... more

Wind Power - Betz's law

Wind power is the conversion of wind energy into a useful form of energy, such as using wind turbines to produce electrical power, windmills for mechanical ... more

Wind Energy

Wind power is the conversion of wind energy into a useful form of energy, such as using wind turbines to produce electrical power, windmills for mechanical ... 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

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

Tractive Force - Steam locomotives

As used in mechanical engineering, the term tractive force can either refer to the total traction a vehicle exerts on a surface, or the amount of the total ... more

Torque - to overcome rolling resistance

Torque, is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as ... more

Mass of pressure Cylindrical vessel with hemispherical ends( capsule)

Pressure vessels are held together against the gas pressure due to tensile forces within the walls of the container. The normal (tensile) stress in the ... 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

Cylinder stress (hoop stress)

In mechanics, a cylinder stress is a stress distribution with rotational symmetry; that is, which remains unchanged if the stressed object is rotated about ... more

Moment of inertia of a thick-walled cylindrical tube ( Axis at the center of the cylinder perpendicular to its height)

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

Potential energy is stored in the crust in the form of built-up stress. During an earthquake a small fraction of the seismic moment is converted into ... 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

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

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

A screw is a mechanism that converts rotational motion to linear motion, and a torque (rotational force) to a linear force. It is one of the six classical ... more

Motor Resonance Frequency

A stepper motor or step motor or stepping motor is a brushless DC electric motor that divides a full rotation into a number of equal steps. The ... more

Energy stored in a capacitor

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

Johnson-Kendall-Roberts (JKR) model of elastic contact between two spheres ( pull-off force)

Contact mechanics is the study of the deformation of solids that touch each other at one or more points.When two solid surfaces are brought into close ... more

The blade root bending moment due to the wind turbine yaw operation. The yaw rate can be calculated for passive yaw, or is defined by the design for active ... 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

Elastic potential energy( with respect to Length)

Elastic energy is the potential mechanical energy stored in the configuration of a material or physical system as work is performed to distort its volume ... more

Brushed DC electric motor - Speed

A brushed DC motor is an internally commutated electric motor designed to be run from a direct current power source. Brushed motors were the first ... more

Screw - distance ratio

A screw is a mechanism that converts rotational motion to linear motion, and a torque (rotational force) to a linear force. It is one of the six classical ... more

Wind turbine angular velocity

The formula for the calculation of the angular velocity of a wind turbine rotor. The definition is according to the IEC 61400-2. ... more

Rod and piston-to-stroke ratio

In a reciprocating piston engine, the connecting rod or conrod connects the piston to the crank or crankshaft. Together with the crank, they form a simple ... more

Energy of damped harmonic motion

Damped harmonic motion is a real oscillation, in which an object is hanging on a spring. Because of the existence of internal friction and air resistance, ... more

Spring constant

Hooke’s law is a principle of physics that states that the force F needed to extend or compress a spring by some distance X is proportional to that ... more

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