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Moment of inertia is defined with respect to a specific rotation axis. The moment of inertia of a point mass with respect to an axis is defined as the product of the mass times the distance from the axis squared. The moment of inertia of any extended object is built up from that basic definition. The general form of the moment of inertia involves an integral.A force acting on a rigid body is a sliding vector: it may be moved along its line of action without changing the effect on the body. With the aid of the notion of the couple moment, we now will investigate how a force may be moved to a parallel line of action. Consider in Fig. 3.7 a force F whose line of action f is assumed to be moved to the line f′, which is parallel to f and passes through point 0. The perpendicular distance of the two lines is given by h. As a first step, the forces F and −F are introduced on the line f′. These two forces are in equilibrium. One of the forces and the originally given force (action line f) represent a couple. The cou- 58 3 General Systems of Forces, Equilibrium of a Rigid Body ple moment is given by its magnitude M(0) = hF and the sense of rotation. The system consisting of force F with action line f′ and couple moment M (0) = h F is statically equivalent to force F with action line f. The quantity M(0) = hF is called the moment of the force F about (with respect to) point 0. The superscript (0) indicates the reference point. The perpendicular distance of point 0 from the action line f is called the lever arm of force F with respect to 0. The sense of rotation of the moment is given by the sense of rotation of force F about 0. FF 0hF=0hF=0 f′ F f f′f M (0)= hF f′ f It should be noted that a couple moment is independent of the point of reference, whereas the magnitude and sense of rotation of the moment of a force depend on this point. Often it is advantageous to replace a force F by its Cartesian components F x = Fx ex and F y = Fy ey (Fig. 3.8). Adopting the commonly used sign convention that a moment is positive if it tends to rotate the body counterclockwise when viewed from above (􏰛), the moment of the force F about point 0 in Fig. 3.8 is given by M (0) = h F .

Gross, Dietmar. Engineering Mechanics 3. Springer. LSU Online Library. Web. 23 Feb. 2016. <javascript:open_win('https://utils.louislibraries.org/cgi-bin/lz0050.x?sitecode=LALUelib?http://libezp.lib.lsu.edu/login?url=http://dx.doi.org/10.1007/978-3-642-30319-7?catkey=4060239')>.

Linear rate springs:

Linear springs are the easiest to understand. When you think of a spring, this is typically what you are thinking of. As the load on the spring increases, the spring compresses an amount directly proportional to that load. So, if the spring is rated at 100lbs per inch, in will compress 2 inches when 200lbs is applied. The following graph describes this relationship which I’m sure you already understand: In general, the most performance oriented and springs designed for racing are going to have a linear rate. The consistent nature of linear rate springs makes the car stable, optimizes traction, and makes the car more predictable for the driver.

Progressive (variable rate springs):

These springs are sometimes called variable Rate springs. The purpose of non-linear springs is to provide more compliance in the suspension over rough surfaces. These springs are designed with low initial spring rates but rapidly increase as the spring is compressed. The theory is that this allows the car to travel smoothly over bumps and road imperfections but still be tight enough to provide good handling and prevent the chassis from bottoming out. Because of this, these springs are popular in aftermarket lowering springs and coilover system intended for use on public roads.

Variable rate springs are easy to spot because the springs are not symmetrical. Typically, one end of the spring is wound tighter than the other end with the more tightly wound end being the softer part of the spring. As the spring is compressed, the soft coils on the tightly wound side will collapse, coming into contact with each other. When this happens, the rest of the spring starts to compress at the second higher rate. Sometimes two separate springs are used at the same time with a special perch in-between them to achieve the desired effect. Depending on the design, many different curves are possible. Some of the possible curves could look like: While progressive rate springs may not be common in road racing, in off-road racing like rallying, they come into their own. In off road forms of racing where suspensions have longer travel, they can be tuned to come into effect when the car lands after a jump and still maintain softness over the general stage.

Progressive springs are not common in road race cars because these cars typically operate on smooth surfaces. On a car designed for smooth tarmac, these types of springs actually decrease performance as they induce some slop into the suspension. Furthermore, high level road race cars do not have enough suspension travel to really take advantage of progressive springs. These cars typically rely on bump stops (which actually is a second spring with an extremely high rate) to keep themselves from bottoming out and to protect their suspension components.

Progressive springs are popular with lowering springs for street use because most cars are street bound. High rate linear springs produce a harsh ride which is undesirable for everyday driving. Everything in cars is a compromise, and you can’t have the highest performance springs without sacrifices some place else – in this case ride quality.

John MIlmont. "Linear vs Progressive Rate Springs." Automotive Thinker. 24 Jan. 2014. Web. 16 Feb. 2016.

History of the Houston Astros Lead

The Houston Astros are an American professional baseball team based in Houston,Texas,that competes in Major League Baseball (MLB). The Astros are a member of the MLB's National League. The Astros are one of two MLB teams based out of Texas, the other being the Texas Rangers. The team began with the name Colt .45s and have gone through several name changes since. The team has been stationed at several diffrent baseball fields in Texas. The most notable field is the Astrodome complex. The team currently resides in Minute Maid Park, a stadium with a retractable roof. The Astros hold zero World Series titles and one national league title.