Use these phrases to explain why you're approaching the person in need of sympathy, if you heard about the problem from someone else. If s/he started the conversation, respond by acknowledging the other person's feelings. "I'm sorry to hear that." "I heard you were going through tough times." "That sounds painful." Some people respond to stress or grief by becoming busier. They may not take the time off to think about their emotional state. Make eye contact and use a phrase that makes it clear you're asking about his/her feelings, not day-to-day life: "How are you feeling?" "How are you coping with everything?" Make it clear that you are on his/her side. Mention friends and family that may also be able to support him/her, reminding him/her that s/he has other people to turn to: "You are in my thoughts." "I am here when you need me." "I'll be in touch later this week about helping out with _____." Avoid the very common "Let me know if there's anything I can do." This actually makes the person have to think of something for you, which they may not feel capable of doing at this time. Some people have trouble expressing emotions, or feel that they are experiencing the "wrong" emotions. Use these phrases to let them know it's okay: "It's okay to cry if you need to." "I accept whatever you need to do right now." "It's normal to feel guilty." (or anger, or whichever emotion the other person just expressed)
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One-sentence summary -- Acknowledge the event or problem. Ask the person how they're coping. Express support. Let the person know that emotions are appropriate.

Though you will still be calculating displacement using a straight line, you will need to find the difference between an object's initial and final location when it moves in an arc. Think of a girl sitting on a merry-go-round. As she spins along the outside of the ride, she will travel in a curved path. Angular displacement seeks to measure the shortest distance between the initial location and final location when an object isn't moving in a straight line. The formula for angular displacement is: = S/r, where "S" stands for linear displacement, "r" stands for radius, and "" represents angular displacement. Linear displacement is how far an object travels along an arc. Radius is the distance an object is from the center of a circle. Angular displacement is the value we are looking for. Remember that radius is the distance from the center of a circle; some problems may give you the circle's diameter, in which case you will need to divide it by 2 to find the radius. Here is a sample problem: A girl rides a merry-go-round. Her seat is at a distance of 1 meter from the center (radius). If the girl moves along an arc length of 1.5 meters (linear displacement), what is her angular displacement? Your equation should look like this: = 1.5/1. This will give you the angular displacement of the object. After dividing 1.5 by 1, you are left with 1.5. The angular displacement of the girl is 1.5 radians. Since angular displacement calculates how much an object has rotated from its original position, it will need to be measured as an angle, not a distance. Radians are units used to measure angles.
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One-sentence summary -- Find angular displacement when an object travels in a curved path. Input the linear displacement and radius values into the equation. Divide linear displacement by the radius.

If you are sending a personal email, there is no need for a signature. A signature block includes information including your title, your contact information, and your company or organization's information. Do not worry about including this information if you are sending an informal or personal email. Instead, just sign your name. Often, your company or organization will require a signature and they will let you know what information they require. Ask your company if they have a standardized signature block they want you to use. If your company does not provide a standard signature block, you can also copy a block from someone else in your organization and replace their contact details with yours. Your signature block should include a few basic things. At minimum, it should have your first and last name, your title, your phone number, and your email address.You may also choose to include your company or organization's logo, website, and links to social media like LinkedIn, YouTube, and Facebook. If your company or organization does not have a standard signature format, follow this basic flow: Put your name first, followed by your title on the next line. Then, add your email and phone number, and put your company or group info last. Try to keep your signature short and simple. Use three or four lines of text. Add a logo instead of typing out your company name, and use a series of social network icons instead of typing out URLs. Be wary of including too much social media information. Links should go to your company's social media information. If your company does not have social media accounts, it is generally not appropriate to link to your own accounts unless expressly told to do so. Most email clients including Gmail and Outlook allow you to save your signature so that you can add it with one click instead of typing it out. Check under your email settings to set up your signature. Many email clients have a simple "Signature" option under the "Settings" tab or icon. Type your signature, add your graphics, and save it for reuse.
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One-sentence summary -- Decide if a signature is necessary. Add your information. Save your signature for repeated use.

If you find yourself getting stuck by the introduction and it is preventing you from writing the rest of your paper, skip it for now. Just write your thesis statement at the top of your paper and start on your body paragraphs. You may find it easier to write your introduction after you finish your essay, after you know what you end up saying with your essay. It is more important to get into a groove with your writing than to write each part in the order that it comes in the essay. An introduction should introduce your topic, state your argument, and provide your reader with the context of your essay. If sentences in your introduction do not help with any of those goals, they are likely unnecessary. A hook, often the very first sentence in your paper, is a sentence or two that "hooks" or grabs the interest of your audience. Commonly used hooks may be good for novice writers, but some college professors think that certain hooks are overused. A few ideas for hooks follow. A statistic (particularly one that seems surprising to the reader) can be a good way to start certain types of papers. Be sure the statistic is from a reliable source, like one from your school's library database. A personal story or anecdote told in detail can draw the reader in. It should, however, be relevant to the topic, and you will need to explicitly connect it to your thesis statement. This may not be appropriate in a formal essay. A quotation from a famous person can be a good lead-in. However, since this is one method that has been overused, try putting a twist on this method by using a surprising quote, contradicting the quote, or using it in a new context. You will also need to connect this to your thesis clearly. Illuminating a paradox or puzzling scenario could draw your reader in by making them question something that is usually taken for granted. Try to avoid introductions that start by giving a dictionary definition of a word and explaining it or by asking a question. Avoid over-used and essentially empty phrases like "from the beginning of time" or "throughout the history of mankind." You will need to write a few sentences that explain the context of your hook and transition into the thesis of your paper. If your hook is long, as with a detailed personal anecdote, this may be a phrase like "this experience has led me to believe that" If your hook is shorter, like a statistic, you will likely need to write 3-4 sentences explaining your statistic and leading up to your thesis statement.
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One-sentence summary --
Consider writing your introduction last. Remember the purpose of an introduction. Write a hook. Transition from your hook to your thesis.