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The centroid of each sub-line with respect to a point of the sub-line is shown in the following figure. Express the centoids with respect to point O, i.e. the origin of the coordinate system, and use Eqs. 9.22 to calculate the centroid of the whole line (bar). To facilitate the calculations, we use a table as follows.
A centroid is the geometric center of a geometric object: a one-dimensional curve, a two-dimensional area or a three-dimensional volume. Centroids are useful for many situations in Statics and subsequent courses, including the analysis of distributed forces, beam bending, and shaft torsion. Two related concepts are the center of gravity, which ...
- What Is "Center of Gravity"?
- Why Do Tall Things Topple Over?
- Why Does Gravity Make Your Body Tip Over?
- What's The Best Way to Balance?
- How Does It Help to Know About Center of Gravity?
Throw a ball in the air and gravity pulls it straight back down. Noteverything moves like this when gravity acts on it. Most objects arenot nice, neat shapes like balls. That means gravity acts on them inmore complex ways. Even so, all objects behave as though their mass(the stuff they're made from) is concentrated at a point called their center of...
Thinking about center of gravity helps us answer questions like this. Stand up straight,then try leaning over to one side. Very quickly you'll reach a pointwhere your whole body feels like it's about to topple over. You'renot actually moving but turning about your ankles. Your headmoves faster than your knees. In fact, your whole body turns aroundy...
Imagine your body is not a single, solid mass but a huge sack ofpotatoes standing upright. Gravity pulls on the whole sack, but italso acts on each potato separately, pulling each one downward. Whenyou lean over to one side, the "potatoes" at the top of your bodywork like a lever, making your top half turn and topple about yourankles. The more you ...
Lower your center of gravity
The lower your center of gravity, the easier it is to keep your balance.If you're sitting on a chair, you can lean over more than if you'restanding up. With your center of gravity low, you can lean further toone side or the other without creating enough turning force to tipyou over. That's why racing cars (and military vehicles like Humvees)are designed with very low centers of gravity: the lower they are tothe ground, the less risk there is that they'll tip over, no matterhow fast they go. P...
Counterbalance
Tightrope walkers use a slightly different trick to master their center ofgravity. If you've ever watched a tightrope walker, you'll havenoticed they never simply walk across the rope. Some stretch theirarms out or carry a long stick or an umbrella. Others crouch down orbend their knees. Still others ride bicycleswith weights danglingsome way beneath them. These balancing aids help to give tightropewalkers more control over their center of gravity. If they can keeptheir center of gravity dire...
Buy time with inertia
Inertia(the tendency still objects haveto stay still and moving objects to keep moving) helps too. A tightrope walker weighs quite a lot. That means theyhave a certain amount of inertia and it takes quite a bit of time fortheir body to move to one side or the other. If they feel themselvestipping, they have enough time to move another part of their body (ora stick or umbrella they're carrying) to the other side. Thatproduces a tipping force in the opposite direction that keeps thembalanced. L...
If you're a skeptic, you might think science is full of useless bits of informationyou never really need to know, but center of gravity isn't one of them. Last winter,the lane where I live froze over completely and turned to a sheet of ice. What's the best way to walk down a frozen street? Assuming you don't have mountaineering boots, the safest wa...
For example, in Figure 7.2.1 the center of gravity of the block is at its geometric center meaning that ˉx and ˉy are positive, but if the block is moved to the left of the y axis, or the coordinate system is translated to the right of the block, ˉx would then become negative. Figure 7.2.1. Location of the centroid, measured from the origin.
This means that the centroid must lie along the line of symmetry if there is one. If a shape has multiple symmetry lines, then the centroid must exist at their intersection. Figure 7.4.1. Centroids lie upon axes of symmetry. Since rectangles, circles, cubes, spheres, etc. have multiple lines of symmetry, their centroids must be exactly in the ...
To determine the center of gravity of the composite body, we need to determine the weight of each sub-body and express the centers of gravity with respect to the origin of one fixed coordinate system. Since is constant for each body, determine its center of gravity according to the formulation derived in Example 9.1.2. The following figure ...
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Chapter. 7. Centroids and Centers of Gravity. A centroid is the geometric center of a geometric object: a one-dimensional curve, a two-dimensional area or a three-dimensional volume. Centroids are useful for many situations in Statics and subsequent courses, including the analysis of distributed forces, beam bending, and shaft torsion.
