Represented Austin Energy, a public electric utility owned by the City of Austin, TX, as lead transaction counsel in connection with its agreement to purchase from Southern Power the Nacogdoches Generating Facility, a 115-MW, wood waste biomass-fueled power plant in East Texas for $460 million.in its $365 million acquisition of Ascendant Group Limited, the parent company of Bermuda Electric Light Company. Served as M&A counsel to Algonquin Power & Utilities Corp.of the 67.5 percent of Lansing equity that it did not already own. The complex cash-and-stock deal involved the purchase by The Andersons, Inc. ![]()
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![]() More, you have the option to select which of the backup files you want to restore. The app's file recovery process is also as fast. It lets you upload your files online within minutes, and though there are a lot of background processes, it didn’t impact the daily computing experience negatively. Aside from backing up your entire drive, it also offers one of the fastest in terms of performance. Fast and SafeĪcronis True Image is arguably the most featured backup tool available today. You need to choose whether you wish to save online or locally. However, you must note that the app does not allow you to choose both options simultaneously. The local backup software is identical to the online version. More, unlike iDrive, wherein you can do so as a bonus, Acronis True Image offers it as one of its core features. If you wish to keep a copy of your entire drive, this app can do it.īut what will impress you the most is that it gives you the option to save your data locally. Acronis True Image can back up even your system files and applications. Some online backup services are limited to media and document files only. More it offers nearly unlimited storage, so if you have thousands of photos, videos, or music files, you can save all of them. ![]() It backs up all of the personal files on your computer to the cloud and keeps them from floods or fires. Here enter true online backup services, such as Acronis True Image. However, as good as they may sound, using your cloud syncing providers to backup all your files may cost too much. These services offer cloud-based storage that copies a set of files or folders while letting you share some files with your contact. You might be familiar with cloud syncing platforms, such as Dropbox, Google Drive, and iCloud. It comes with a wide range of options and features perfect for hardcore PC users. It offers a robust solution for protecting files and disk images using cloud storage. Acronis True Image is one of the best computer backups available today. That is why it is a good thing that there are backup tools available for download. But what makes it devastating is the fact that we sometimes cannot prevent data loss from happening. Losing a file on your computer can be annoying, especially if it is important. ![]() Your mission: skillfully command a battleship through the Empire’s now chaotic, violent clusters ––where one wrong move could be your last–– as you try to reactivate the OMNIs and save the future of all humankind. You are a clone of Admiral Ellys Idaho, a weapon fashioned from flesh, the best Imperial Admiral ever to battle in the stars and you have just been awoken on this planet by its strange and darkly-humorous Guardian, Kaliban, the last functional OMNI to exist. But somewhere in a far corner of the Galaxy is Gehenna, a planet of ice and rock and a top-secret facility that is the pinnacle of Imperial Tech and also humanity’s last chance. Crying Suns’ visual style blends simplicity with beauty. And humankind, having long since lost the ability to survive on its own, is dangerously close to extinction. The OMNIs, god-like machines that did everything for their human masters, have mysteriously shut down. ![]() A dark and disturbing atmosphere inspired by our favorite S-F universes ( Foundation, Dune, Battlestar Galactica)Īfter 700 years of peace and prosperity, the Galactic Empire has suddenly been shattered into pieces.A deep and dramatic storyline structured in 6 chapters 7 Ever felt the icy stillness of the vacuum of space and responsibility of restoring an empire to its former glory bearing down on your shoulders while casually blowing up pirates Crying Suns.Tying in to both tip 5 and tip 1, as soon as your sensors allow it, make sure you fully mouse over the star map to check over those outposts. Always look ahead It’s the best way to repair your squadrons. ![]() Tactical fights between battleships and their squadron fleets It is much better to spend your scrap in outposts, risk every event, and sell any surpluses when you can.You’ll learn about the ruling houses of the Empire. FTL’s plot is simply an excuse to hang the gameplay upon, but Crying Suns has a fully-developed world and lore that is spun out to the player over many journeys into its dark reaches. Sure, it goes hand in hand with the grim world but still. Nevertheless, this is the hook that Crying Suns offers over the likes of FTL: a story-driven adventure. Personally, I think they failed big time. Space exploration in a procedurally-generated universe Graphics: While FTL had a cute 2D graphic, Crying Suns opted for a more realistic dystopian-sci-fi look, with plenty of effects, while still retaining a pixel-art effect.Make sure to check out our forum threads for Forager, Slay the Spire, and Crying Suns. The game combines elements of space exploration, resource management, and tactical combat, offering players an engaging and immersive experience as they command. In this story rich experience inspired by Dune and Foundation, each successful run will uncover the truth about the Empire… and yourself as well. Crying Suns is available on the App Store for iOS here and on Google Play for Android here. Crying Suns is a tactical rogue-lite that puts you in the role of a space fleet commander as you explore a mysteriously fallen empire. ![]() Unlimited downloads, playlist downloads, and subtitle downloads are supported by all paid plans. Premium 4K Video Downloader features are the main reason why it’s considered among the best YouTube downloaders. You don’t need to register an account, pay anything upfront, and won’t have to deal with watermarked content. The basic version of this app allows you to pull audio from your clips, create slideshows, and convert any YouTube video to MP3. It rocks a free version with somewhat limited features and three premium subscription plans.Īll 4K Video Downloader versions support single-video downloads at varying speeds (the free version is the slowest and the Pro is the fastest). 4K Video Downloader ĤK Video Downloader is one of the safest YouTube video downloaders that, as its name suggests, can be used to capture up to 4K videos and clips. Both Movavi Screen & Video Recorder apps are premium, and since bulk downloads aren’t supported, Viddly is a much better-rounded option. Overall, this is an excellent alternative to Viddly for users that want full control over the clips/videos they want to download. Movavi also offers a sophisticated Video Editor app that works in synergy with its Screen Recorder program it offers over 180 filters, the ability to add background music, segment content, and more. With the Movavi Screen Recorder, you can perform simple editing operations on the clips. You can fine-tune the recording parameters by selecting the desired recording area mute, lower, or raise the volume, as well as trim content as you go. What makes Movavi stand out is its array of editing and customizing tools. This function works similarly to standard downloads - once you set the parameters, Movavi will begin recording your screen, so all you need to do is ensure that the clip you wanted to take is rolling.Ĭlips that are taken with Movavi cover both audio and video of clips and videos running on the screen, but sadly, batch downloads and processing are not supported. ![]() This program offers several features that can simulate that process, though, especially the scheduled recording feature. Unlike Viddly, Movavi’s screen recorder cannot be used to download YouTube videos in a “traditional” sense. The quality of the captured clips or videos is identical to the original quality of playback videos/clips, which is both a drawback and a benefit in itself. Movavi offers an advanced screen recorder tool that can be used to capture any YouTube video in real time. Viddly Premium Alternatives Movavi Screen recorder If you want to make use of Viddly’s finest features, you can subscribe to Plus Yearly, or buy the Plus Lifetime both are highly affordable and well worth the money. Quality-wise, Viddly is among the handful of apps that support 8K Full Ultra HD video quality, which is supported by both paid plans.įrom support for 8K FUHD downloads at 60 frames per second, automatic URL downloads, batch downloads, and YouTube live stream recording, as well as cross-device compatibility and YouTube channel downloads, the premium version of Viddly is easily the best YouTube downloader in the current market. This can save hours of your time that would otherwise be wasted on finding, copying, and queuing links for download. Unlike other YouTube video downloaders, the suggestions are not limited to a dozen results.Īnother key advantage of Viddly YouTube downloader is that it can be used to download not just playlists but entire channels. The built-in YouTube video search bar saves you time looking for videos in your browser instead, you can find any clip within Viddly and instantly download it. Aside from removing sponsored content, Viddly Plus unlocks a variety of important upgrades. The free version features ads, although you can remove them by upgrading to the Viddly Plus Plan. This program can be downloaded and used for free indefinitely the features its free version is supplied with are superior to contemporary free-to-use alternatives, offering decently quick download speeds, support for the majority of popular video formats, URL-based downloading, Viddly’s proprietary search bar, and more. Its robust features, simple UI, and downloading speed make it one of the best software applications in this field. Viddly is one of the leading YouTube downloader/converter apps for Windows. The purpose of this article is to provide a detailed review of Viddly and its alternatives, the benefits this app offers in comparison to both free and premium competitors, and to ultimately declare which YouTube downloader is the best in the market. It is a remarkably fast app with an intuitive user interface and a virtually non-existent learning curve. Performance-wise, it has easy yet strong tools capable of downloading the highest-quality videos and audio. Viddly is regarded as one of the best YouTube downloader & converter apps. ![]() Sleep Buddy is a toddler sleep training system that is designed to help your tot learn when he or she should stay in bed. Sleep Buddy – Toddler Sleep Training System My 8-year-old has this and loves this, but you know who loves it more? Our toddler! While it’s not the best at teaching how to tell time, it’s perfect for an outer space bedroom. Diggin Thomas The Tank GoGlow Sleep Training Clockįans of Thomas the Tank will love this 2 in 1 bedtime training clock and night light. Perfect for your little night owl, this portable night light works as a night light and glows green in the morning when it’s okay to get out of bed. Onaroo Night Owl Portable Night-Light with OK to Wake! Little Tikes Discover Sounds alarm clock is the perfect toddler clock for your younger toddlers. Pink, pretty and a high rating on Amazon! The Kid Sleep My First Alarm Clock will help your little one wake up when it’s time to wake up and help teach your toddler how to read a clock. When the red light is on it is time to sleep – when the green light is on it is time to wake up. With the Stoplight Sleep Enhancing Toddler Alarm Clocks toddlers know if it’s time to get up by looking at the stoplight. The light turns green when it’s okay to wake up mommy and daddy. American Innovative Teach Me Time Talking Alarm Clock and NightlightĪdorable child’s bedside alarm clock, time-teaching tool and dual-color nightlight all in one. Ok to Wake Owl toddler clock has a face that glows soft yellow to comfort toddlers at night and then lights green (“OK to wake!”) in the morning at a time programmed by the parent. OK To Wake! Owl With Night-Light & Music, Nap Timer This is definitely one of the funner clocks for toddlers. Your toddler will love this clock as it also doubles as a night light. How cool is this? Not an alarm clock, but this will help you in your sleep training your toddlers! You can take the glow balls with you – no more dark trips to the bathroom for a potty break. The Zazoo photo alarm clock is also a digital photo frame! 4. Use one of the pre-loaded songs for the alarm tone or wake to any song of your choice. ![]() There are several options for the audio alarm tone including ringing, beeping or waking to music. The clock comes with display options that may include the time only or time and date. Use your PhotoClock as a traditional clock with an audio alarm. You can customize how your child wakes up with the Zazoo photo clock. The kids know they are allowed to get up when the sun comes up. In the morning, at the designated time, the last star and the big star disappear, and the sun comes out as the face color changes to yellow. The stars disappear over the night, so when your child wakes up in the night, they instantly know how long they have until morning by how many stars are left. The Glo-Clock Sleep Trainer clock has a pleasant glow of light – not to bright and the concept is unique. Set this bedside alarm clock next to your tot’s bed and let sleep training begin. OK to Wake toddler alarm clock, color changing night-light timer teaches children to stay in bed longer in the morning so parents get more sleep (at least that’s the plan!). ![]() Some toddler clocks even have a time out timer. Here is a fabulous assortment of the best toddler alarm clocks that have different functions to help with sleep training. I hope they work well as you sleep train your toddler.Īs you transition your toddler from the crib to a big boy bed (or big girl bed), it’s time to introduce the alarm clock. I have had many friends recommend these and am glad to share these here. One of the hardest challenges when I had to get the kids to child care and we had a strict morning routine was finding a kid friendly alarm clock. I survived the toddler years with our 2 older kids and am now going through it now with another 2 toddlers! You can survive these years (at least, I hope – these last 2 are quite challenging.) It’s all about finding things that work for you. Here is a round up of the best toddler alarm clocks. ![]() Parenting toddlers is all kinds of crazy, if they get a little more sleep – that will give mom and dad more sleep as well! Sleep training your toddler? Check out these toddler alarm clocks that will help a child who can’t tell time understand when it’s okay to get ouf of bed. If you have toddlers that have a hard time with sleeping, this post is for you! Technology and Kids – One of our most popular posts involves trying to get kids to sleep and stay in bed with kids alarm clocks for toddlers. In order to keep you up-to-date with the best toddler alarm clocks, we update this post regularly. ![]() Nancy DeMoss is genius at using God’s truth to shed light on how to overcome Satan’s crafty ways and walk in God’s grace, forgiveness, and abundant life like never before. It creates a darkness in our lives that prevent us from seeing things for what they really are. Lies get us in trouble because, once we start believing them, we become blinded to the fact that we’re being deceived in the first place. I can seriously keep going-the list is endless! ![]() A real game changer, it has brought me face to face with the lies I believed about myself (that struggle shouldn’t be part of my story), lies about others (their grass is for sure greener), lies about sin (I can handle it it won’t get that bad), lies about success (it should go quicker it shouldn’t be a process), and lies about consequences (it won’t impact me the way I’ve been warned it will). I’ve been telling so many people about this amazing book. I still have lots more to read and learn myself! Oh, and one more thing, some Bible studies automatically come with DVDs and/or download instructions, others only come in the Leader Kits (and some have no videos)-details you might want to check into as you consider each study. I get this question all the time, so I wanted to compile a list to send people to for reference purposes. I know I am not the end-all-be-all of small group studies, I just wanted to provide a resource for the BTD community. There could very well be MORE out there that I’m just not aware of, all of which could be perfectly amazing options for your small group to go through. Please know that this list only covers what I had time to decipher for myself and feel is best for the BTD community. After doing some research, it seems safe to say that any Bible study from the following list of authors would be a great option for your small group: Priscilla Shirer, Beth Moore, Jen Wilkin, She Reads Truth, Kay Arthur, Elisabeth Elliot.Īnd gosh, I’m also pretty nervous publishing this list because I don’t want to offend anyone by not including them on the list. I wanted to list them out as I didn’t include ALL their studies in the list. Conducive to a group setting The List: Best Small Group Bible Studiesīefore going into the list, I want to note that among the comments, there were several Bible study authors who came up continually – authors with multiple studies. So each of these on this list is chock-full of Scripture too and encourages you to read through different parts of the Bible as you go through itĥ. After all, it should be a BIBLE study guide rather than a compilation of personal stories and opinions. Truth-filled – It’s important to me that a Bible study is heavy on encouraging you to read ACTUAL Scripture. Rather than keeping things on the surface, I think it’s important that a Bible study pushes you individually (and your group when you meet) to face hard truths and dig deep into how we’re living our lives. Challenging – Asking hard questions that help you grow in your personal walk/relationship with Christ is essential. So you’d feel like you were learning and reading from someone who GETS you and your strugglesģ. I wanted to make sure the “voice” of each author is one that is easy to understand. Culturally relevant and relatable – Not all Bible studies are easy to relate to. Otherwise, people will be seriously misled.Ģ. Anyone who sets out to teach the Bible should commit to being as faithful to Scripture as possible. Proclaiming God’s word is serious business. Our duties as Christians include biblical discernment-which can only be done by examining what a person says and comparing it with Scripture. Biblically sound – Let’s not be taken in by a public figure who is confident, assertive, and appears to be biblical. How Did We Pick The Books On The List?įor each of the studies included in the list, it was extremely important to me that they met the following criteria:ġ. In addition to the ones I collected from Team BTD (and friends), I added a few I had personally heard about AND actually gone through myself, and then started the vetting process. ![]() I also got several DMs from people after mentioning I was compiling a list on my IG stories. (I also got emails) I read through every single one of them, making a list of every single study mentioned. When I polled Team BTD on their favorite (group) Bible studies, I got A LOT of different responses from women (and some men too!) in different stages of life and with different backgrounds too. I intend to keep this updated as I learn more and discover additional studies. ![]() And after getting this question time and time again, I decided it was time I dedicate an entire resource page on my blog to answering this question. One of my MOST frequently asked questions is what the best small group bible studies are or whether or not I recommend any. ![]() Combining uncompromising product quality with customer-inspired innovation and value, Cobalt has earned an international reputation for unmatched customer satisfaction through its World Class Dealer Network. Orders for the Model A36BR are currently being accepted, with initial deliveries scheduled for early 2019 via Cobalt’s World Class Dealer Network.Ībout Cobalt: Headquartered in Neodesha, KS, Cobalt Boats LLC, is a publicly owned, industry-leading manufacturer of luxury family day boats. “Continuing with our original concept of a small premium yacht that does everything well, the A36BR maintains the high level of luxury, quality, performance, beauty and customer-centric luxury that made the A36 such an immediate success, while adding even more day-boat features,” said Paxson St. Noteworthy options range from a bow sail shade to a protected cockpit pop-up TV and a full-function galley. Other thoughtful comfort touches include optional stadium bow seating with inward-facing armrests, dedicated self-draining storage areas under the bow cushions, and a cabin that offers sleeping space for two with additional storage that’s hidden cleverly behind a sliding door. Matching the original A36 coupe’s performance and handling, the A36BR shares an extended running surface that makes both models exceptionally smooth and stable at high speeds. In addition to more bow seating, the A36BR provides a quiet running experience via improved sound insulation and sealing in the engine compartment and cabin. Maintaining the distinctive look of the A36 coupe, the A36BR offers a level floor for comfortable cockpit seating, along with a deep and spacious bow area that gives it its name. Browse to see imagery of our luxury boats in action, read stories from our community of owners, learn about the latest innovations we’re developing, and more. ![]() 12, 2018 (GLOBE NEWSWIRE) - Premium luxury manufacturer Cobalt Boats has introduced a refined new version of its popular A36 crossover line, the A36BR, which incorporates a spacious bow with a deck that simultaneously allows for functional interior ergonomics and a greater variety of day-boat features. Enhanced Bow Rider design maintains the exterior look of the popular A36 deluxe crossover while increasing bow and cockpit seating and upgrading the interior layout and features ![]() If you were an administrator, every process was running with the keys to your system. Every application, every process ran in the same security context as the logged in user. Remember when Windows Vista was released? Remember the backlash against the interface changes, driver support, and User Account Control (UAC)? It was pretty brutal! I will gladly admit (as I did then) that I really liked Vista. Let’s make life a little easier! A Little UAC History In this article, we are going to walk through User Account Control (UAC) and AppLocker, and best practices for implementing them. In our organization, we went from regularly having 50+ new viruses a day, to zero infections over a two year period. Rest assured, this pattern can be broken – and broken with two built-in technologies. You get infected, you clean it, you get infected (again), you clean it (again). If you have something to tell about the subject - you are welcome in comments.For many, computer viruses and malware are a way of life. I don’t see any chances for Applocker to become a popular whitelisting technology in near future. Even though, SRP has few disadvantages (comparing with Applocker), better OS support makes more sense and is more decisional than anything else. Windows 8 is second Windows OS generation where we can use Applocker, however technology support is limited again. I spend some time to move Applocker rules to SRP. ![]() I was really disappointed when I noticed, that Applocker is partially supported there (cannot enforce rules). Recently I bought a new notebook and installed Windows 8 Pro. The table displays the most important features that we may want to see in any whitelisting technology. Also I would like to show you a quick table that displays feature support in Applocker and SRP:Įrror messages when application is blocked On the other hand, SRP lacks in built-in security filtering, as the result we have to maintain multiple group policy objects (GPO) to allow various software usage scenarios depending on a user permissions. Also Applocker has a serious (in certain cases - blocking) bug: you cannot create path rules for network locations (or mapped drives). Windows 8 RT, Professional, Ultimate, Enterpriseįeel the difference.Windows 7 Professional, Ultimate, Enterprise.Windows Vista Business, Ultimate, Enterprise.Windows Server 2012 (all editions, except server core installation).Here is a full list of operating systems that supports Applocker: In practice, SRP has better support and sometimes is better than Applocker. And companies have to maintain both technologies - Applocker for modern systems and SRP for other systems. Thus, it is almost impossible for companies to use Applocker as a unified whitelisting technology, because there are systems which do not support Applocker. ![]() In small business (SMB) it is easier to keep similar operating systems (say, Windows 7 Pro clients and SBS servers) than for large enterprises. There are no business decisions to limit Applocker to top desktop editions (Ultimate and Enterprise). Windows 7 Pro has Applocker console where you can create rules and export them, you cannot enforce them. This was a bad move, because small business market not always can purchase Enterprise editions and commonly uses Professional edition (a replacement for Vista Business). Why not Applocker?Įven though, Microsoft actively promoted Applocker between IT Pros, the technology remained behind the scene, because it was available only in Windows 7 Ultimate and Enterprise editions. I successfully used Applocker on my personal computers when I got an access to Windows 7 (previously I used SRP) as a free and powerful malware protection mechanism. For example, we can export and import rules in XML format, create rule collections, added new useful variables, nice rule creation wizard and built-in security filtering. As the result, we got SRPv2 called Applocker, which was introduced in Windows 7 and Windows Server 2008 R2.įrom the first look it was a nice replacement for SRP with some useful additions. Microsoft attempted to make SRP more flexible, user-friendly and simple in configuration and usage. Due to various reasons, SRP didn’t become a popular technology that was used by systems administrators (not talking about home users). SRP is original Microsoft whitelisting technology which was introduced in 2001 (with Windows XP release). Not all know that this is not something new (as Microsoft promotes), but a next generation of Software Restriction Policies (SRP). Hello folks! Today I want to share some personal opinions about one Windows whitelisting technology - Applocker, especially about the future. Update : clarified Applocker support on server core installations. ![]() Proceed to the right and turn into B Street at the diner. With Agent Ray proceed to the right and pick up a speck of dust fom the street in front of the prestige realtors building (to the left of the van), then talk to the pigeons again who ask for a WC-67 tube. Leave and enter the sheriffs office upstairs to talk to him. Go into the coroner's office to learn about your forensic analysis tools and the pillow factory fire. Talk to the pigeons, then move on to the right to enter Thimbleweed Park and proceed until you meet the Sheriff. Go to the right to be freed by the sheriff. Open the red box and call Deborah Ingram under 1550 using the dime we just found (you can look up the number with Agent Reyes in the phone book). Go to the left and find more specks of dust in front of a gate and on the floor under a red box. Note that the Quickie Pal store is right above you, then go back to where you woke up. Walk into the tunnel, pick up a speck of dust and a dime. Click on her icon to make her come back to her senses. You will see that Agent Ray is available again. You can enter the post office and talk to the employee, but for now go further to meet the old lady who cursed Ransome. ![]() Pick up a speck of dust in front of the liquor store. Then go back to A street to trigger another cutscene. Afterwards, proceed to where your partner was attacked to find her notebook. You can make a stop at the cemetary and find Chuck's grave. Go further into the dark (trash can) and get knocked down.Īs Agent Rayes walk up to the city. Note that ThimbleCon87 takes place at the hotel that we might be able to attend once we have a map. Enter the alley behind the diner and pick up a speck of dust. As you keep going to the right the sheriff tells you to get a map. Enter the Quickie Pal and pick up another speck of dust from the floor in front of the clerk. ![]() Enter the bathroom of the Quickie Pal and use the light switch. Leave the diner and leave the town to the right triggering a cut scene. Having fulfilled all requirements you can now enter the stage and get cursed to finish Ransome's introduction. With them return to Joe and obtain the joke book. He demands interest, so return and pick up the swear jar money to obtain the missing $138. Go to Joe and try to get your jokebook back. Proceed to your dressing room, use makeup and hair gel. In hard mode you need to find the combination. In casual mode you can just open the safe to obtain $1000 in cash. Pick up two notes and a card from the cupboard. Look at your todo list and put on your clown nose (you might have to obtain it from the clown doll first). Enter the diner to the right and talk to Sandy to trigger Ransome's subplot. Find another speck of dust in front of the electronics store. Turn into A Street and enter Nickel News and talk to the woman. Pick up the tuna can (useless item), the Atari cartridge, the circus poster and the plastic rings as you go to the right. Go to the left, open the gate and proceed upstairs. Search the body to find a hotel keycard and take the empty Whiskey bottle. Give the polaroid film to Agent Ray, then switch to her, insert it into the camera and take a picture of the body. If you want to add any pieces of information I've missed, please feel free to. I haven't had an opportunity to play the game myself, yet, so please take everything here with a grain of salt. This is a preliminary walkthrough written before the release of the game and thus highly prone to error and incomplete. Now we’ll calculate the area moment of inertia for the rectangular section centered on this line CD. We would then assume that one of the lines will pass through the rectangular section’s base. We’ll start with one rectangular section ABCD, as shown in the figure below. I y = hb 3/ 12 Calculating Moment of Inertia of Rectangle Section We’ll get the following equation as a result: (3) A Centroidal Axis Perpendicular to Its Baseīy alternating the dimensions b and h from the first equation given above, we can determine the moment of inertia of a rectangle by taking the centroidal axis perpendicular to its base. D is said to be the perpendicular distance between the x and x’ axes.I x = moment of inertia in arbitrary axis.If we recognize the moment of inertia of the non-centroidal axis with respect to a centroidal axis parallel to the first, we can find it here. The parallel axis theorem could be used to calculate the area moment of inertia of any shape present in any parallel axis. It is seamlessly determined by applying the Parallel Axis Theorem because the rectangle centroid is located at a distance equal to h/2 from the base. The moment of inertia of a rectangle has been expressed as follows when an axis passes through the base: (2) Moment of Inertia of Rectangle An Axis Passing Through Its Base The rectangle width (a dimension parallel to the axis) has been denoted by b, and the height is denoted by h (dimension perpendicular to the axis). In the particular instance where the axis passes through the centroid, the moment of inertia of the rectangle is given as follows: When sizing linear systems, the most important use for mass moment of inertia is probably in motor selection, where the ratio between the load inertia and the motor inertia is a critical performance factor.(1) Moment of Inertia of Rectangle An Axis Passing Through Its Centroid The mass moment of inertia equation for a point mass is simply:įor a rigid body, the mass moment of inertia is calculated by integrating the mass moment of each element of the body’s mass: Mass moment of inertia, like planar moment, is typically denoted “I,” but unlike planar moment, the units for mass moment of inertia are mass-distance squared (slug-ft 2, kgm 2). It has the same relationship to angular acceleration that mass has to linear acceleration. Mass moment of inertia (also referred to as second moment of mass, angular mass, or rotational inertia) specifies the torque needed to produce a desired angular acceleration about a rotational axis and depends on the distribution of the object’s mass (i.e. I = planar moment of inertia Mass moment of inertia Cantilever beam with a concentrated load at the free end Unsupported shafts are also analyzed using beam deflection calculations. In linear systems, beam deflection models are used to determine the deflection of cantilevered axes in multi-axis systems. The planar moment of inertia of a beam cross-section is an important factor in beam deflection calculations, and it is also used to calculate the stress caused by a moment on the beam. The equation for polar moment of inertia is essentially the same as that of planar moment of inertia, but the distance used is distance to an axis parallel to the area’s cross-section. Second moment of area can be either planar or polar. Polar moment of inertia describes an object’s resistance to torque, or torsion, and is used only for cylindrical objects. Planar moment of inertia is expressed as length to the fourth power (ft 4, m 4). If it’s unclear which type of moment is specified, just look at the units of the term. Terminology varies, and sometimes overlaps, for planar moment and mass moment of inertia. Planar moment of inertia (also referred to as second moment of area, or area moment of inertia) defines how an area’s points are distributed with regard to a reference axis (typically the central axis) and, therefore, its resistance to bending. ![]() ![]() But it’s critical to know which type of inertia-planar moment of inertia or mass moment of inertia-is given and how it affects the performance of the system. ![]() Moment of inertia is an important parameter when sizing and selecting a linear system. |
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