Explanation Given information: The mass of the clamp is m B . The mass of the hoop is m h . Calculation: Sketch the kinematics of the hoop as shown in Figure 1. Refer to Figure 1. Calculate the acceleration at A ( a A ) as shown below. a A = r α → Calculate the acceleration ( a B / A ) as shown below. a B / A = r α ↘ Calculate the acceleration at B ( a B ) as shown below. a B = a A + a B / A Substitute r α → for a A and r α ↘ for a B / A . a ¯ B = ( r α → ) + ( r α ↘ ) Hence, ( a B ) x = r α and ( a B ) y = r α . Calculate the moment of inertia ( I ¯ ) as shown below. I ¯ = m h r 2 Sketch the Free Body Diagram and kinetic diagram for the hoop and the clamp as shown in Figure 2. Refer to Figure 2. Calculate the angular acceleration ( α ) as shown below. Apply the Equations of Equilibrium of moment about C as shown below. ∑ M C = I G α + m a d W B r sin θ = [ I ¯ α + m h a A r + m B r α ( r + r cos θ ) + m B r α sin θ ( r sin θ ) + m B r α cos θ ( r + r cos θ ) ] Substitute m B g for W , r α for a A , r α for ( a B ) x , r α for ( a B ) y , and m h r 2 for I ¯

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9781259639272

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 16.2, Problem 16.115P

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The expression for the angular acceleration of the hoop in terms of mB, mh, r, and θ.

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Chapter 16.2, Problem 16.114P

Chapter 16.2, Problem 16.116P

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Chapter 16 Solutions

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

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The expression for the angular acceleration of the hoop in terms of m B , m h , r , and θ .

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The expression for the angular acceleration of the hoop in terms of mB, mh, r, and θ.

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