Angular Momentum of a Conical Pendulum?
A small metallic bob of 2.9kg is suspended from the ceiling by a thread of negligible mass. The ball is then set in motion in a horizontal circle.
Given: Length of thread 2.8m, angle between thread and vertical 21 degrees, and g=9.8, calculate the magnitude of the angular momentum of the bob about the supporting point.
Now, remember momentum = mass * velocity. Then it shouldn’t surprise you that angular-momentum = moment_of_intertia * angular_velocity.
So, what’s the moment of inertia? We’ll assume the bob is a point particle, therefore the moment of inertia = mass*(radius)^2. When calculating moments of inertia, the radius is always the distance between the center of mass of the object, and the axis about which it’s rotating. (This will take a bit of trig.)
Then, recall velocity = angular_velocity * radius. Now then, angular_velocity = velocity / radius. And your velocity is the speed at which the bob is going around the circle, and the radius is again measured between the center of mass of the bob and the axis of rotation.
To calculate the velocity, figure out with what force the bob is being pulled toward the center. If this were just a regular old two dimensional pendulum, with what force would it want to fall towards equilibrium from this point (caused by the tension)? Well, that force is going to be the same here, except we know that because it’s moving in a circle, this force must be matched by the centripetal force.
And recall centripetal_force = mass * velocity^2 / radius. The radius is, again, the distance between the center of mass of the bob, and the axis of rotation. Now, you can solve for velocity, and plug it in above.
I hope this helps!
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Finding The Right Craft Threads
Threads are important when crafting quilts. You will need certain threads that match your fabric, as well as suitable supplies and needles. Yet, when you consider matching threads to your fabric, you will also need to consider a few other details.
Types of threads:
You have choices of thread, including rayon, buttonhole-twists, silk, all-purpose, cotton, nylon wool, monofilament, metallic, exceptionally fine, mercerized cotton and so on. To consider threads, first you must ask if you are intending to create your quilt by hand, or machine? Do you prefer to darn or to bast?
If you are sewing fabric piece onto fabric, using shaped pieces to form your pattern, you may want to choose the monofilament Nylon Thread. On the other hand, if you are sewing your fabric by hand, sewing the pieces to form a pattern then the silky threads, or the all-purpose threads may be a good option.
If you are hand crafting you may want to consider other threads than the all-purpose. For instance, you may get more from the threads with polyester cores and wrapped in cotton. The polished 100$ finished cotton is also available. If you use the thread with finished polish, it will reduce wearing if you are sewing by hand. The thread will help you stitch smoothly without worrying about tangles, creases, etc.
TIP: Buy beeswax cake to minimize tangles.
Once you finish choosing your threads, you will need to create a craft basket. The basket will include thimbles, scissors both for cutting paper and fabric, (a few pairs) threader, hand needles, pencils, tailor chalk, seam ripper, and a measuring device. You will also need straight quilter pins, pincushion, glue stick, and a few safety pins. (Large)
Once you gather your basket, you may want to add supplies, such as rotary cutters, iron/board, masking tape, press cloth, spray bottle, graphing/tracing paper, hoops and frames, colored pencils, plastic sheet, ruler, cutting mat, and so on. You may even want to toss in a few band-aids to cover those pokes and sticks you will get from hand sewing your quilt.
When you purchase your needles choose the “household assortment” kits to sum up your sewing needs. Otherwise, needle sizes are opposite, i.e. if you purchase the larger numbers, you get a smaller needle.
If you are hand, sewing you may want to consider “sharp” needles. The needles make it easy to stitch through heavy-duty material. In stores you might look for sharps, or “household needles.” To shorten your field trip on the mind tangler, just purchase a couple of 8′s and 9′s, as well as the variety packages. The needles with slotted eyes are called the “easy-threader,” which you can use also if you have problems using other needles.
You will need the seam ripper to correct your mistakes. The rippers will cut your thread, yet you should practice before you use them on the actual quilt, especially if you are new at making quilts.
You will need markers as well as a ruler to measure seams, patterns, fabric, etc. The needle threader will make it easy to thread. Remember the tips of some needles are small, making it difficult to get the thread pulled through the eye. Thimbles are designed to reduce the need for band-aids. You will need to test a few thimbles to fit them to your fingers.
In all, each item in your basket will help you complete your quilt. If you are new at quilting, visit your library, or go online to learn more steps to help you create a fashionable design, or a traditional style if You Choose.
About the Author
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