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Engineering Mechanics: Dynamics, Study Pack by Russell C. Hibbeler

By Russell C. Hibbeler

The Dynamics learn Pack used to be designed to assist scholars increase their examine talents. It includes 3 research components—a chapter-by-chapter overview, a free-body diagram workbook, and an entry code for the significant other site.

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1 PRINCIPLE OF LINEAR IMPULSE AND MOMENTUM • The principle of linear impulse and momentum is obtained from a time integration of the equation of motion and is described by the equation mv1 + t2 F dt = mv2 . 0) t1 – Linear Momentum. Each of the two vectors of the form L = mv is referred to as the particle’s linear momentum. It’s magnitude is mv and its direction is the same as that of the velocity v. – Linear Impulse. The integral I = F dt is referred to as the linear impulse. This is a vector quantity which measures the effect of a force during the time the force acts.

It is sometimes referred to as the moment of momentum. • Scalar Formulation. The magnitude of HO is given by (HO )z = (d)(mv). – d is the moment arm (perpendicular distance from O to the line of action of mv). – Direction of HO is defined by the right-hand rule. – Units for (HO )z are kg · m2 /s or slug · f t 2 /s. z HO O P x y d mv 30 Chap. 15 Kinetics of a Particle: Impulse and Momentum • Vector Formulation. If the particle P is moving along a space curve and r is a position vector drawn from point O to the particle P : H O = r × mv .

3 EQUATIONS OF MOTION: TRANSLATION • Rectilinear Translation Fx = m (aG )x Fy = m (aG )y MG = 0 or summing moments about A = G : MA = ( M k )A Here, (Mk )A represents only the moments of the two components of maG about A (since, in translation IG α = 0). • Curvilinear Translation Fn = m (aG )n Ft = m (aG )t MG = 0 or summing moments about B = G : MB = ( Mk )B Here, (Mk )B represents only the moments of the components m (aG )n and m (aG )t about point B (since, in translation IG α = 0). PROCEDURE FOR SOLVING PROBLEMS Kinetic problems involving rigid-body translation can be solved using the following procedure: • Free-Body Diagram – Establish the x, y or n, t inertial frame of reference and draw the free-body diagram in order to account for all the external forces and couple moments that act on the body.

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