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In classical mechanics, impulse (symbolized by J or Imp〔Beer, F.P., E.R. Johnston, Jr., D.F. Mazurek, P.J. Cornwell, and E.R. Eisenberg. (2010). ''Vector Mechanics for Engineers; Statics and Dynamics.'' 9th ed. Toronto: McGraw-Hill.〕) is the integral of a force, F, over the time interval, t, for which it acts. Since force is a vector quantity, impulse is also a vector in the same direction. Impulse applied to an object produces an equivalent vector change in its linear momentum, also in the same direction.〔(Impulse of Force ), Hyperphysics〕 The SI unit of impulse is the newton second (N·s), and the dimensionally equivalent unit of momentum is the kilogram meter per second (kg·m/s). The corresponding English engineering units are the pound-second (lbf·s) and the slug-foot per second (slug·ft/s). A resultant force causes acceleration and a change in the velocity of the body for as long as it acts. A resultant force applied over a longer time therefore produces a bigger change in linear momentum than the same force applied briefly: the change in momentum is equal to the product of the average force and duration. Conversely, a small force applied for a long time produces the same change in momentum—the same impulse—as a larger force applied briefly. : The impulse is the integral of the resultant force (''F'') with respect to time: : ==Mathematical derivation in the case of an object of constant mass== Impulse J produced from time ''t''1 to ''t''2 is defined to be : where F is the resultant force applied from ''t''1 to ''t''2. From Newton's second law, force is related to momentum p by : Therefore, : where Δp is the change in linear momentum from time ''t''1 to ''t''2. This is often called the impulse-momentum theorem.〔See, for example, section 9.2, page 257, of Serway (2004).〕 As a result, an impulse may also be regarded as the change in momentum of an object to which a resultant force is applied. The impulse may be expressed in a simpler form when the mass is constant: : where :F is the resultant force applied, :''t''1 and ''t''2 are times when the impulse begins and ends, respectively, :''m'' is the mass of the object, :v2 is the final velocity of the object at the end of the time interval, and :v1 is the initial velocity of the object when the time interval begins. The term "impulse" is also used to refer to a fast-acting force or impact. This type of impulse is often ''idealized'' so that the change in momentum produced by the force happens with no change in time. This sort of change is a step change, and is not physically possible. However, this is a useful model for computing the effects of ideal collisions (such as in game physics engines). Impulse has the same units and dimensions as momentum. In the International System of Units, these are . In English engineering units, they are . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Impulse (physics)」の詳細全文を読む スポンサード リンク
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