THE CENTER OF GRAVITY
The center of gravity is a geometric property of any object. The center of gravity is the average location of the weight of an object. We can completely describe the motion of any object through space in terms of the translation of the center of gravity of the object from one place to another, and the rotation of the object about its center of gravity if it is free to rotate. In flight, rockets rotate about their centers of gravity.
Determining the center of gravity is very important for any flying object. How do engineers determine the location of the center of gravity for a rocket which they are designing?
In general, determining the center of gravity (cg) is a complicated procedure because the mass (and weight) may not be uniformly distributed throughout the object. The general case requires the use of calculus which we will discuss at the bottom of this page. If the mass is uniformly distributed, the problem is greatly simplified. If the object has a line (or plane) of symmetry, the cg lies on the line of symmetry. For a solid block of uniform material, the center of gravity is simply at the average location of the physical dimensions. For a rectangular block, 50 X 20 X 10, the center of gravity is at the point (25,10, 5) . For a triangle of height h, the cg is at h/3, and for a semi-circle of radius r, the cg is at (4*r/(3*pi)) where pi is ratio of the circumference of the circle to the diameter. There are tables of the location of the center of gravity for many simple shapes in math and science books. The tables were generated by using the equation from calculus shown on the slide.
For a general shaped object, there is a simple mechanical way to determine the center of gravity:
- If we just balance the object using a string or an edge, the point at which the object is balanced is the center of gravity. (Just like balancing a pencil on your finger!)
- Another, more complicated way, is a two step method shown on the slide. In Step 1, you hang the object from any point and you drop a weighted string from the same point. Draw a line on the object along the string. For Step 2, repeat the procedure from another point on the object You now have two lines drawn on the object which intersect. The center of gravity is the point where the lines intersect. This procedure works well for irregularly shaped objects that are hard to balance.
If the mass of the object is not uniformly distributed, we must use calculus to determine center of gravity. We will use the symbol S dw to denote the integration of a continuous function with respect to weight. Then the center of gravity can be determined from:
cg * W = S x dw
where x is the distance from a reference line, dw is an increment of weight, and W is the total weight of the object. To evaluate the right side, we have to determine how the weight varies geometrically. From the weight equation, we know that:
w = m * g
where m is the mass of the object, and g is the gravitational constant. In turn, the mass m of any object is equal to the density, rho, of the object times the volume, V:
m = rho * V
We can combine the last two equations:
w = g * rho * V
then
dw = g * rho * dV
dw = g * rho(x,y,z) * dx dy dz
If we have a functional form for the mass distribution, we can solve the equation for the center of gravity:
cg * W = g * SSS x * rho(x,y,z) dx dy dz
where SSS indicates a triple integral over dx. dy. and dz. If we don't know the functional form of the mass distribution, we can numerically integrate the equation using a spreadsheet. Divide the distance into a number of small volume segments and determining the average value of the weight/volume (density times gravity) over that small segment. Taking the sum of the average value of the weight/volume times the distance times the volume segment divided by the weight will produce the center of gravity.
The meaning of social media
Social media refers to applications and websites – the collective of online communications channels – that enable people, companies, and other organizations to create and share content on social networking sites and blogs.
There are many applications (apps) and websites that are dedicated to social networking, forums, social bookmarking, microblogging, products/services reviews, social curation (Digg, Reddit), wikis, virtual worlds, and other types of social media.
Individuals, companies, and other organizations through social media create, share or exchange a range of things, including ideas, pictures, videos, career interests, opinions, jokes, complaints, experiences, and items of news. Both companies and individuals use social media platforms for marketing purposes too.
Social media is a term that we currently throw around a lot. Its meaning has widened considerably since its usage in language started to become popular. If we use the term to describe sites like Twitter and Facebook, and also Digg and Reddit, then its meaning starts becoming rather vague.
Social media has many meanings
As commonly happens when a term is overused, social media is beginning to have different meanings for different people. People who have a more restricted view on what it defines tend to give it the same meaning as social networking – websites such as Twitter, Facebook, etc. Others will tell you that blogs are not included in its definition.
Elise Moreau, writing in webtrends.com, has an interesting and, in my opinion, accurate approach to the meaning of social media. She starts by looking at each word ‘social’ and ‘media’ individually:
– Social: refers to people interacting with each other by sharing information.
– Media: refers to channels of communications, including TV, radio, newspapers, magazines, billboards, and the Internet.
So, if we pull the meanings of these two separate terms together, we get:
“Social media are web-based communication tools that enable people to interact with each other by both sharing and consuming information.”
Social media depends on web-based and mobile technology to create highly interactive platforms through which individuals and other entities can share, discuss, create, co-create and modify user-generated content.
It is significantly changing how we all communicate with each other and tell our network members about ourselves. Technoself studies focus on these changes.
Social media vs. traditional media
Social media differs considerably from traditional media – physical newspapers and magazines, plus TV and radio. While the former is a dialogic transmission system (many viewers and many creators all communicate with each other) traditional media operates under a monologic transmission system (there is just one source and many receivers).
Studies show that people are spending more and more time each week on social media sites, in many cases at the cost of other types of sites, and definitely at the cost of offline activities and even sleep. For advertisers, these types of sites and blogs have become extremely important.
In 2015, Nielsen.com reported that three of the most popular online brands worldwide were social media-related – Facebook, YouTube, and Wikipedia. Globally, we spend 22% of all our time online on these types of sites.
Three-quarters of global consumers with Internet access visit social networks or blog sites. The average visitor in 2015 spent 24% more time visiting these sites compared to 2014.
American business magnate, Bill Gates, who co-founded Microsoft and became the richest person in the world, once said: “The PC has improved the world in just about every area you can think of. Amazing developments in communications, collaboration, and efficiencies. New kinds of entertainment and social media. Access to information and the ability to give a voice to people who would never have been heard.”
Negative effects
Several negative effects have been associated with social media, especially regarding privacy, information overload and Internet fraud.
Angry or emotional exchanges can eventually lead to serious and sometimes dangerous confrontations in the real world outside of the Internet.
Young and older naïve people can be lured by predatory pedophiles, murderers and rapists.
Studies suggest that social networking sites may have a negative effect on individuals’ self-esteem and self-worth. One study found that people with a greater social comparison orientation – they compare their own lives with those of their family members, friends and work colleagues – tend to use these sites more heavily compared to individuals with low social comparison orientation.
Take Facebook for example; most members tend to post positive aspects of their lives; this makes other people wonder why their own lives are not as fulfilling or exciting. This, psychologists say, can push susceptible people into depression and other self-esteem issues.
Online and mobile phone bullying has become a serious problem for both children and adults across the world.
Positive effects
Social networking and blogging sites are great places to document memories, advertise oneself, form friendships, and learn about and explore things.
In social networking sites we all have the possibility of becoming content creators. Networked individuals who create content can reach a wider audience.
If used effectively, it can positively affect people’s social standing and help them gain political support, which can lead to influence on issues they find important. Participants in the 2011 Tunisian revolution, for example, used Facebook to organize meetings and protest actions.
Many websites, such as Wiki, are the result of individuals creating and collaborating with other network individuals.
According to a survey carried out by Pew Internet Research, ‘networked individuals’ are involved in considerably more creation activities compared to their non-networked counterparts.
Networked individuals typically take part in the following content creation activities:
- Writing material on Facebook and other social networking sites. Sixty-five percent of internet users say they do this.
- Sharing photographs – done by 55% of Internet users.
- Reviewing products and contributing to rankings – 37% do this.
- Creating tags of content – 33%.
- Posting their comments on third-party blogs or websites – 26%.
- Remixing material gathered online into a new creation: 15% say they do this with text, audio, video or photographs.
- Creating a blog or working on one.
On many occasions, social media has been used to help in the search for missing persons.
According to socialmediadefined.com, Social Media is:
“The future of communication, a countless array of internet-based tools and platforms that increase and enhance the sharing of information. This new form of media makes the transfer of text, photos, audio, video, and information in general increasingly fluid among internet users. Social Media has relevance not only for regular internet users but business as well.”
(MBTs) Malawi blood transfusion
Why should people donate blood? Safe blood saves lives. Blood is needed by women with complications during pregnancy and childbirth, children with severe anaemia, often resulting from malaria or malnutrition, accident victims and surgical and cancer patients.
Be safe and enjoyable
10 tips for happy kids
The first thing that needs to be said is that kids don’t have to be happy all the time. They need to learn to deal with feelings of sadness, anger, frustration, loss, jealousy, envy, disappointment … all those “negative” emotions we all experience. That’s how they become resilient to the ups and downs of life they will inevitably face. They also need to learn it’s not always all about them; that they are in this life with others who matter as much as they do.
What we want our kids to be is generally happy and grounded in self-confidence and respect for themselves and others, with the ability to feel empathy while still knowing they can ask for and often receive what they want. We all know a generally happy child when we see one.
Of course, for most of us, the automatic answer to the question of what makes children happy would be love, so that’s a given — as long as it’s unconditional. Love is the big one, but then there are everyday little things that can also make a child’s life more comfortable, secure and happy. Here are 10 we think are worth keeping in mind.
1. They eat on time, and they eat well
A no-brainer? Not to everyone. Some people think that eating after school, for example, will “spoil dinner”. And “on time” doesn’t just mean mealtimes. Active little people need snacks in between to refuel their brains and growing bodies. Blood-sugar lows can result in poor concentration and inability to focus and settle, which can have consequences at school.