(a) Explanation Calculation: Write the equation of centroidal radius of gyration ( k ¯ ) of the rigid body using the equation: I ¯ = m k ¯ 2 k ¯ 2 = I ¯ m Here, I ¯ is the mass moment of inertia and m is the mass of the rigid body. Consider the point C is the instantaneous center with corresponding to center of percussion P and the distance between points G and P is d p . Consider the principle of impulse and momentum. Syst Momenta 1 + Syst Ext Imp 1y2 = Syst Momenta 2 Sketch the impulse and momentum diagram of the rigid body as shown in Figure (1). Refer Figure (1). Consider the components parallel to F Δ t . 0 + F Δ t = m v ¯ (1) Here, F is the force acting on the rigid body at P, Δ t is the time required to attain velocity v ¯ . Take moments about G . 0 + d p ( F Δ t ) = I ¯ ω (2) Here, ω is the angular velocity of rigid body (b) To determine Show that if the center of percussion were located at C the instantaneous center of rotation would be located at P .

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Author: BEER

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 17.2, Problem 17.68P

(a)

To determine

Show that the instantaneous center of rotation C of the body is located on line GP at a distance GC=k¯2GP on the opposite side of G.

(b)

To determine

Show that if the center of percussion were located at C the instantaneous center of rotation would be located at P.

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Chapter 17.2, Problem 17.66P

Chapter 17.2, Problem 17.69P

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Show that the instantaneous center of rotation C of the body is located on line GP at a distance G C = k ¯ 2 G P on the opposite side of G .

Solution Summary: The author shows the instantaneous center of rotation C of the body is located on line GP at a distance GC=stackrel k2GP on the