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Battling Top Design:

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What makes a good Intro Project competitive outcome wide design space low tinkering coefficient low math ability use of SolidWorks/Matlab/Excel low material cost low fabrication skill link to science related topics safety

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Coil Gun Ranking competitive outcome 2 wide design space 2 low tinkering coefficient 2 low math ability10 use of SolidWorks/Matlab/Excel5 low material cost2 low fabrication skill9 link to science related topics9 safety5 SCORE46

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"Battling Top" Ranking competitive outcome 7 wide design space 7 low tinkering coefficient 7 low math ability10 use of SolidWorks/Matlab/Excel8 low material cost8 low fabrication skill9 link to science related topics9 safety10 SCORE74

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Catapult Ranking competitive outcome 9 wide design space 7 low tinkering coefficient 7 low math ability10 use of SolidWorks/Matlab/Excel6 low material cost6 low fabrication skill7 link to science related topics9 safety5 SCORE66

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Rules Core Material limit – 2"x2"x2" aluminum cube – plus anything you want to screw/fasten into it like a shaft for launching Design own launcher (acrylic possible) Rip cord < 24" Arena will be some bowl shaped thing – anyone have a snow disk?

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Tops involve angular rotation, a challenging engineering topic Moment of inertia From Wikipedia, the free encyclopedia In classical mechanics, moment of inertia, also called mass moment of inertia, rotational inertia, polar moment of inertia of mass, or the angular mass, (SI units kg·m²) is a measure of an object's resistance to changes to its rotation. It is the inertia of a rotating body with respect to its rotation. The moment of inertia plays much the same role in rotational dynamics as mass does in linear dynamics, describing the relationship between angular momentum and angular velocity, torque and angular acceleration, and several other quantities. The symbol I and sometimes J are usually used to refer to the moment of inertia or polar moment of inertia.classical mechanicsSIrotationinertiarotational dynamicsangular momentumangular velocitytorqueangular acceleration

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Moment of Inertia Overview The moment of inertia of an object about a given axis describes how difficult it is to change its angular motion about that axis. Therefore, it encompasses not just how much mass the object has overall, but how far each bit of mass is from the axis. The farther out the object's mass is, the more rotational inertia the object has, and the more force is required to change its rotation rate. For example, consider two hoops, A and B, made of the same material and of equal mass. Hoop A is larger in diameter but thinner than B. It requires more effort to accelerate hoop A (change its angular velocity) because its mass is distributed farther from its axis of rotation: mass that is farther out from that axis must, for a given angular velocity, move more quickly than mass closer in. So in this case, hoop A has a larger moment of inertia than hoop B.

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The moment of inertia of an object can change if its shape changes. Figure skaters who begin a spin with arms outstretched provide a striking example. By pulling in their arms, they reduce their moment of inertia, causing them to spin faster (by the conservation of angular momentum).angular momentum

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Scalar moment of inertia Consider a rigid body rotating with angular velocity ω around a certain axis. The body consists of N point masses m i whose distances to the rotation axis are denoted r i. Each point mass will have the speed v i = ωr i, so that the total kinetic energy T of the body can be calculated asrigid bodyangular velocitykinetic energy In this expression the quantity in parentheses is called the moment of inertia of the body (with respect to the specified axis of rotation). It is a purely geometric characteristic of the object, as it depends only on its shape and the position of the rotation axis. The moment of inertia is usually denoted with the capital letter I: It is worth emphasizing that r i here is the distance from a point towards the axis of rotation, not towards the origin. As such, the moment of inertia will be different when considering rotations about different axes.

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Similarly, the moment of inertia of a continuous solid body rotating about a known axis can be calculated by replacing the summation with the integral:integral where r is the radius vector of a point within the body, ρ(r) is the mass density at point r, and d(r) is the distance from point r to the axis of rotation. The integration goes over the volume V of the body.radius vectordensity

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Ycm, height of center of mass Ycm is the average height of mass distribution making up the top. if you wanted to balance it from a string, sideways, Ycm is where you would attach the string: Ycm

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Stability Coefficient The overall stability of the top, based on some approximations, is indicated by: stability = Rg/Ycm – Radius of Gyration divided by – the height of the center of mass Implications: – increase Rg, stability ++ – decrease Ycm, stability ++

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The calculations are daunting If we wanted to try a number of different designs, it would take forever Fortunately engineers use computer tools such as Matlab to speed the development of design

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