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Speeds and feeds - feed rate

The phrase speeds and feeds or feeds and speeds refers to two separate velocities in machine tool practice, cutting speed and feed rate. They are often ... more

Surface Feet per Minute (SFM)

Surface feet per minute (SFPM or SFM) is the combination of a physical quantity (surface speed) and an ... more

Spindle Speed

Surface feet per minute (SFPM or SFM) is the combination of a physical quantity (surface speed) and an ... more

Material Removal Rate

Machining is any of various processes in which a piece of raw material is cut into a desired final shape and size by a controlled material-removal process. ... more

Machinability Index

The term machinability refers to the ease with which a metal can be cut (machined) permitting the removal of the material with a satisfactory finish at low ... 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

Critical Speed of a Rotating Shaft - Dunkerley's method

In solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating ... more

Critical Speed of a Rotating Shaft - Rayleigh–Ritz method

In solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating ... more

Angular velocity

In physics, the angular velocity is defined as the rate of change of angular displacement and is a vector quantity (more precisely, a pseudovector) which ... more

Volumetric flow rate

The volumetric flow rate is the volume of fluid which passes through a given surface per unit time. Fow velocity in fluid dynamics or drift velocity in ... 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

Angular Frequency

In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, radian frequency, ... more

Volumetric flow rate (parallel to the unit normal)

volumetric flow rate, (also known as volume flow rate, rate of fluid flow or volume velocity) is the volume of fluid which passes per unit time. The only ... 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/

Motor Torque constant

The constant K_v (motor velocity constant, or the back EMF constant) is a value used to describe characteristics of electrical ... more

Air-to-cloth ratio

The air-to-cloth ratio is the volumetric flow rate of air flowing through a dust collector’s inlet duct divided by the total cloth area in the ... more

Speed

In everyday use and in kinematics, the speed of an object is the magnitude of its velocity (the rate of change of its position); it is thus a scalar ... more

Power - rotational systems (torque)

Power is the rate at which work is done. It is equivalent to an amount of energy consumed per unit time. Power in mechanical systems is the combination of ... more

Power-mechanics (Velocity)

Power is the rate at which work is done. It is equivalent to an amount of energy consumed per unit time. Power in mechanical systems is the combination of ... more

FPM to CFM Calculator

Online FPM to CFM unit converter calculator helps to convert cubic feet per minute from feet per ... more

Speed of Sound (air, ideal gases) - relative to the mass of a single molecule

The speed of sound is the distance travelled per unit time by a sound wave propagating through an elastic medium. The SI unit of the speed of sound is the ... more

Speed of Sound (air, ideal gases)

The speed of sound is the distance travelled per unit time by a sound wave propagating through an elastic medium. The SI unit of the speed of sound is the ... more

Specific Impulse

Specific impulse (usually abbreviated Isp) is a way to describe the efficiency of rocket and jet engines. It represents the force with respect to the ... more

Diametral pitch (transverse) - gears

A gear or cogwheel is a rotating machine part having cut teeth, or cogs, which mesh with another toothed part to transmit torque, in most cases with teeth ... more

Sommerfeld Number

In the design of fluid bearings, the Sommerfeld number (S), or bearing characteristic number, is a dimensionless quantity used extensively in hydrodynamic ... more

Speed of Sound in Solids - long rods

The speed of sound is the distance travelled per unit of time by a sound wave propagating through an elastic medium.
The speed of sound for ... more

Petroff's Law - Bearing coefficient of friction

In the design of fluid bearings, the Sommerfeld number (S), or bearing characteristic number, is a dimensionless quantity used extensively in hydrodynamic ... more

Angular Velocity - related to linear velocity

In physics, the angular velocity is defined as the rate of change of angular displacement and is a vector quantity (more precisely, a pseudovector) which ... more

Thrust (with cross section area)

Thrust is a reaction force described quantitatively by Newton’s second and third laws. When a system expels or accelerates mass in one direction, the ... more

Speed of Sound (air, ideal gases) - relative to molar mass

The speed of sound is the distance travelled per unit time by a sound wave propagating through an elastic medium. The SI unit of the speed of sound is the ... more

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