Many people assume that the terms “centre of mass” and “centre of gravity” are synonymous, but this is not the case.
Centre of mass is the point at which the distribution of mass is equal in all directions, and does not depend on gravitational field. Centre of gravity is the point at which the distribution of weight is equal in all directions, and does depend on gravitational field.
A toy bird balances when a pivot is placed at its centre of gravity.
The centre of mass and the centre of gravity of an object are in the same position if the gravitational field in which the object exists is uniform. In most cases this is true to a very good approximation: even at the top of Mount Everest (8848 metres) the gravitational field strength is still 99.6% of its standard value. You are unlikely ever to experience a difference between centre of mass and centre of gravity, as the gravitational field in which you find yourself is extremely uniform.
But if the gravitational field strength were greater towards your feet and weaker towards your head, then your centre of gravity would be below your centre of mass, perhaps somewhere around your knees. If the gravitational field strength were greater towards your head, and weaker towards your feet, then your centre of gravity would be above your centre of mass, perhaps somewhere around your shoulders.
The object on the left, in a uniform gravitational field, has overlapping centres of gravity and mass. For the object on the right, in which the gravitational field is stronger towards its base, the centre of gravity is below the centre of mass. Approaching a black hole the gradient of the gravitational field would be infinitely “steep”, leading to an incredible difference in gravitational field and death by spaghettification for anyone falling into a black hole.
The kinetic energy of an object moving in a straight line is easy to understand:
where is kinetic energy, is the mass of the object and is the object’s velocity.* If the mass of the object doubles, the kinetic energy doubles; and if the object’s velocity double the kinetic energy is quadrupled.
Kinetic energy is the energy that an object has due to the fact that it is moving, and therefore an object that is rotating must have kinetic energy. But if it’s rotating, staying in one place, then its velocity is zero and thus we can’t use the equation above.
The kinetic energy of a rotating object is given by:
where is the rotational kinetic energy, is the angular velocity (i.e. the angle turned through divided by the time taken, measured in degrees per second or radians per second). The complicated part of the equation is , which is the moment of inertia.
The moment of inertia can be thought of as the rotational equivalent of mass; the degree to which an object resists a change in its (rotational) motion. The moment of inertia depends on the shape of the object and the way it rotates. For example: the moment of inertia of a rod rotating about its centre, and a rod rotating about its end, are very different.
The moment of inertia of the rod on the left, rotating around its end is , where is the mass of the rod and is its length. The moment of inertia of the rod on the right that rotates around its centre is and thus if the rods have the same lengths and masses, and rotate at the same rate, the kinetic energy of the rod on the left will be four times greater.
MrReid.org launched on 30th August 2007. In 2012 I published a Five Year Review, and last year I reviewed 2012-2013, and I thought I’d follow up this year with a review of 2013-2014.
September, like many months this past year, was a quiet one for posts. I looked at where all the elements came from, the differences in the order of subjects, objects and verbs in sentences in various languages, and finally worked out the difference between “tons” and “tonnes”.
Full September archive
I was quite pleased with a post about tritium illumination and telomeres and aging, but my favourite post from October was one about the different types of average. I also wrote about an actual method of turning lead (or something else) into gold.
Full October archive
I liked all my posts from November. The post about different sorting algorithms was probably a bit too long, and could maybe have been a bit clearer, but the ones on the different gases used when breathing underwater and on RAID array types were just right.
Full November archive
The post about the EURion Constellation and counterfeit money was easily my favourite from December, and one of my favourites from the whole year. I also liked Earth Sandwich and the post about inequality and the Gini Coefficient.
Full December archive
There was nothing really outstanding from the month of January, but I did enjoy researching Unconventional Nuclear Weapons.
Full January archive
February was very quiet, with only two posts: one on converting from miles to kilometres by using the Fibonacci sequence which was more popular than I’d expected it to be, and one on decibel weighting and the difference between white and grey noise.
Full February archive
March was not a good month for MrReid.org.
April was much better than March, in that I actually made some posts. MrReid.org joined Twitter, and I wrote another personal favourite post discussing what “Five Sigma” data is. I also corrected a very common misconception, writing about the difference between real and apparent weightlessness.
Full April archive
May was another busy month, with a definite typographic theme towards the end. My personal favourite was Why Tokyo Looks Different From Space, but I was also pleased with Ranking Ratings and UPC Barcodes.
Full May archive
An amazing coincidence in June, when an issue I wrote about in a MrReid.org post (Cousins or Siblings?) came up in an A Level biology final exam question a few days later. I also wrote about where space starts, and the shape of rocket engines and the creation of “shock diamonds”.
Full June archive
July wasn’t a brilliant month, because I was very busy at work. I’m still not quite sure I explained why we can’t get all the way to absolute zero quite well enough, but it’s a post I quite like.
Full July archive
I found The Composition of Earth’s Atmosphere with Elevation very interesting, but I have a feeling I might be the only one. I was also very interested by hydraulic fuses, and I finally worked out the difference between an assault rifle and a carbine. I also explained why it feels hotter when the air is more humid.
Full August archive
Here’s to 2014-15. I hope you’ll keep reading.
Propellers and impellers both provide thrust, but do it in different ways.
A propeller is a fan which propels a fluid by pushing against it: it converts rotational motion into linear motion. An impeller is a rotor that produces a sucking force, and is part of a pump. A propeller is always “open” and an impeller is always “closed” (as it has to draw fluid into something).
L-R: Impeller and propeller
Human beings judge how warm they are by how quickly heat leaves the body (we have specialised cells called thermoreceptors that do this job), and maintain temperature by controlling sweating. As sweat evaporates from the skin, it takes heat away from the body and therefore the rate of evaporation affects the rate of heat loss.
When the air is very humid, it is more difficult for evaporation to take place, and therefore humidity affects people’s perception of the temperature: when the air is very humid it feels warmer than it really is. Humidex is an index used by Canadian meteorologists to calculate this apparent temperature.
The dew point is the temperature at which water condenses out of the air and is linked to the relative humidity. If the relative humidity is 100% then the dew point is equal to the current temperature; when the current temperature is below the dew point then water will leave the air (the dew point cannot be higher than the current temperature).
As you can see, as the dew point increases the perceived temperature increases. When the air temperature is 20ºC and the dew point is also 20ºC then the perceived temperature will be 27.6ºC.
The hottest and most humid parts of the world are the coastal areas around the Arabian Peninsula. On July 8th 2003 in Dharan, Saudi Arabia the air temperature was 42.2ºC with a dew point of 35ºC; this yields a humidex of an almost-unbearable 68.9ºC. If we combined the hottest recorded temperature of 56.7ºC in Death Valley, California with this Saudi Arabian dew point record that would yield a humidex of 83.4ºC, which would have killed people: luckily the Death Valley area is a desert valley and the dew point is usually quite low.