(a) Explanation Given information: The radius ( r ) of disk is 250 mm. The length ( l ) of the rod AB is 650 mm. The rod is displaced ( θ m ) for the position of 2 ° . Assume the acceleration due to gravity ( g ) is 9.8 m/s 2 . Calculation: Show the free body diagram equation as in Figure (1). Write the expression for the mass moment of inertia ( I ¯ ) : I ¯ = 1 2 m r 2 The angle ( α ) is equal to the angular acceleration θ ¨ . Write the expression for the tangential acceleration ( a t ) : a t = l α Substitute θ ¨ for α . a t = l θ ¨ The external forces in the system are tension in the force due to the mass of the disk. The effective couple in the system is I ¯ α . Take moment about B in the system for external forces. ( ∑ M B ) e x t e r n a l = − m g l sin θ For small oscillation sin θ ≈ θ , ( ∑ M B ) e x t e r n a l = − m g l θ Take moment about B in the system for effective forces. ( ∑ M B ) e f f e c t i v e = I ¯ α + m a t l The disk is free to rotate and is in curvilinear translation so, I ¯ α is equal to zero. Substitute 0 for I ¯ α and l θ ¨ for a t . ( ∑ M B ) e f f e c t i v e = 0 + m ( l θ ¨ ) l = m l 2 θ ¨ Equate the moment about B in the system for external and effective forces (b) To determine The magnitude of the maximum velocity ( v m ) B of point B assuming that the disk is riverted to the rod at A .

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

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ISBN: 9781260916942

Author: BEER

Publisher: MCG

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Chapter 19.2, Problem 19.60P

(a)

To determine

The magnitude of the maximum velocity (vm)A of point A assuming that the disk is free to rotate in a bearing at A.

(b)

To determine

The magnitude of the maximum velocity (vm)B of point B assuming that the disk is riverted to the rod at A.

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Chapter 19.2, Problem 19.59P

Chapter 19.2, Problem 19.61P

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Chapter 19 Solutions

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.3P Ch. 19.1 - Prob. 19.4P Ch. 19.1 - Prob. 19.5P Ch. 19.1 - Prob. 19.6P Ch. 19.1 - Prob. 19.7P Ch. 19.1 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - Prob. 19.9P Ch. 19.1 - Prob. 19.10P

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The magnitude of the maximum velocity ( v m ) A of point A assuming that the disk is free to rotate in a bearing at A .

Solution Summary: The author shows the free body diagram equation as in Figure (1). Write the expression for the mass moment of inertia and the tangential acceleration.

Concept explainers

The magnitude of the maximum velocity (vm)A of point A assuming that the disk is free to rotate in a bearing at A.

The magnitude of the maximum velocity (vm)B of point B assuming that the disk is riverted to the rod at A.

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Chapter 19 Solutions