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The constant K_M (motor size constant) is a value used to describe characteristics of electrical motors.
The motor constant is winding independent ... more
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
In orbital mechanics, mean motion (represented by ) is a measure of how fast a satellite progresses around its elliptical orbit. The mean motion is the ... more
Nodal precession is the precession of an orbital plane around the rotation axis of an astronomical body such as Earth. This precession is due to the ... more
The gear ratio of a gear train, also known as its speed ratio, is the ratio of the angular velocity of the input gear to the angular velocity of the output ... more
The Euler’s pump and turbine equations are most fundamental equations in the field of turbo-machinery. These equations govern the power, efficiencies and ... more
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
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
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the ... more
For a given torque and angular speed, the rotating horsepower may be calculated
... more
CPU power dissipation is the process in which central processing units (CPUs) consume electrical energy, and dissipate this ... more
Eb/N0 (the energy per bit to noise power spectral density ratio) is an important parameter in digital communication or data transmission. It is a ... more
In physics and engineering, the time constant, usually denoted by the Greek letter (tau), is the parameter characterizing the response to a step input of ... more
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the ... more
Central processing unit power dissipation or CPU power dissipation is the process in which central processing units (CPUs) ... more
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
Mechanical components – as transmission gear and bearings – generates a mechanical loss that reduces the power transferred from the motor shaft ... more
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
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
Terrestrial Time (TT) is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of ... more
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
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves ... more
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis. The unbalanced torque on a body along axis of rotation ... more
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the ... more
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
and for 300 r.p.m
The moment of inertia of one blade will be that of a thin rod rotated about its end.
The total I is four times this moment of inertia, because there are four blades. Thus,
and so The rotational kinetic energy is
Solution for (b)
Translational kinetic energy is defined as
To compare kinetic energies, we take the ratio of translational kinetic energy to rotational kinetic energy. This ratio is
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:
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/
Solar cell efficiency is the ratio of the electrical output of a solar cell to the incident energy in the form of sunlight. The energy conversion ... more
A flywheel is a rotating mechanical device that is used to store rotational energy. Flywheels have a significant moment of inertia and thus resist changes ... more
Solar cell efficiency is the ratio of the electrical output of a solar cell to the incident energy in the form of sunlight. The energy conversion ... more
The gear ratio of a gear train, also known as its speed ratio, is the ratio of the angular velocity of the input gear to the angular velocity of the output ... more
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 in seawater depends ... more
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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?