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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
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
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
In the gravitational two-body problem, the specific orbital energy (or vis-viva energy) of two orbiting bodies is the constant sum of their mutual ... more
An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total ... more
An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total ... more
Parallel axis theorem ( Huygens –Steiner theorem) , can be used to determine the mass moment of inertia or the second moment of area of a rigid body about ... 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
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 body mass index (BMI), or Quetelet index, is a heuristic proxy for human body fat based on an individual’s weight and ... more
The body mass index (BMI), or Quetelet index, is a heuristic proxy for human body fat based on an individual’s weight and ... more
Variable-mass systems, (like a rocket burning fuel and ejecting spent gases), are not closed and cannot be directly treated by making mass a function of ... more
barycentre; from the Greek βαρύ-ς heavy + κέντρ-ον centre) is the center of mass of two or more bodies that are orbiting each other, or the point around ... more
Gravitational waves are disturbances in the curvature (fabric) of spacetime, generated by accelerated masses, that propagate as waves outward from their ... more
The Biot number (Bi) is a dimensionless quantity used in heat transfer calculations. Gives a simple index of the ratio of the heat transfer resistances ... more
In astrodynamics an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time. ... more
Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. Radiation pressure implies an interaction between ... 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/
The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around ... more
A collision is an isolated event in which two or more moving bodies (colliding bodies) exert forces on each other for a relatively short time. Collision is ... more
In celestial mechanics, the standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of the ... more
“Clearing the neighbourhood around its orbit” is a criterion for a celestial body to be considered a planet in the Solar System. This was one ... more
In celestial mechanics, the Lagrangian points (also Lagrange points, L-points, or libration points) are positions in an orbital configuration of two large ... more
In celestial mechanics, the Lagrangian points (also Lagrange points, L-points, or libration points) are positions in an orbital configuration of two large ... more
The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around ... more
Two objects in space orbiting each other in the absence of other forces are in free fall around each other. The motion of two objects moving radially ... more
In astrophysics, the Darwin / Radau equation gives an approximate relation between the moment of inertia factor of a planetary body and its rotational ... more
In astronomy, Kepler’s laws of planetary motion are three scientific laws describing the motion of planets around the Sun.
1.The orbit of a ... more
In astronomy, Kepler’s laws of planetary motion are three scientific laws describing the motion of planets around the Sun.
1.The orbit of a ... more
Due to the self-induction effect, electrostatic energy behaves as having some sort of momentum and “apparent” electromagnetic mass, which can increase the ... 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?