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Optical magnification is the ratio between the apparent size of an object (or its size in an image) and its true size, and thus it is a dimensionless ... more
Depth of field (DOF), or depth of focus, is the distance between the nearest and farthest objects in a scene that appear ... more
Converging lens in air will focus a collimated beam travelling along the lens axis to a spot (known as the focal point) at a distance “f” from ... more
The depth of focus (or depth of field) is a lens optics concept that measures the tolerance of placement of the image plane (the film plane in a camera) in ... more
In optics, the f-number (sometimes called focal ratio, f-ratio, f-stop, or relative aperture) of an optical system is the ratio of the lens’s focal ... more
The angular resolution may be converted into a spatial resolution,by multiplication of the angle (in radians) with the distance to the object. For a ... more
Angular resolution or spatial resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, ... more
A lens is a transmissive optical device which affects the focusing of a light beam through refraction. A simple lens consists of a single piece of ... more
The depth of focus (or depth of field) is a lens optics concept that measures the tolerance of placement of the image plane (the film plane in a camera) in ... more
In optics, the f-number (sometimes called focal ratio, f-ratio, f-stop, or relative aperture) of an optical system is the ratio of the lens’s focal ... more
In optics, particularly as it relates to film and photography, depth of field is the distance between the nearest and farthest objects in a scene that ... more
In optics, particularly as it relates to film and photography, depth of field (DOF) is the distance between the nearest and ... more
In optics, particularly as it relates to film and photography, depth of field (DOF) is the distance between the nearest and ... more
In optics, particularly as it relates to film and photography, depth of field (DOF) is the distance between the nearest and ... more
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the ... more
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the ... more
Aperture is a “hole” or an opening through which light travels. The aperture of an optical system is the opening that determines the cone angle ... more
In photography, exposure is the amount of light per unit area (the image plane illuminance times the exposure time) reaching a photographic film, as ... more
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
In photography, exposure is the amount of light per unit area (the image plane illuminance times the exposure time) reaching a photographic film, as ... more
Pixels per inch (PPI) (or pixels per centimeter (PPCM)) is a measurement of the pixel density ... more
Using the Pythagorean theorem, for 3 different screen resolutions:
Using the Diagonal Resolution from the previous formula we calculate the PPI for 3 corresponding screen sizes :
Results:
10.1 inch tablet screen of resolution 1024×600 : 117.5PPI
21.5 inch PC monitor of 1080p resolution : 102.46PPI
27 inch PC monitor of 1440p resolution : 108.78PPI
On 2-D displays, such as computer monitors and TVs, the display size (or viewable image size or VIS) is the physical size of the ... more
On 2-D displays, such as computer monitors and TVs, the display size (or viewable image size or VIS) is the physical size of the ... more
In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can ... more
In optics, the f-number (sometimes called focal ratio, f-ratio, f-stop, or relative aperture) of an optical system is the ratio of the lens’s focal ... more
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
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/
Pixels per inch (PPI) (or pixels per centimeter (PPCM)) is a measurement of the pixel density ... more
Gravity gradiometry is the study and measurement of variations in the acceleration due to gravity. The gravity gradient is the spatial rate of change of ... more
A lens is a transmissive optical device which affects the focusing of a light beam through refraction. A simple lens consists of a single piece of ... more
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PPI can be calculated from knowing the diagonal size of the screen in inches and the resolution in pixels (width and height). This can be done in two steps