(a) Explanation Given information: The mass of the circular plate ( m ) is 4 kg. The impulsive force ( F Δ t ) is − ( 2.4 N ⋅ s ) k . The radius of the circle ( r ) is 180 mm. The distance between the BG ( b ) is 150 mm. Calculation: Calculate the moment of inertia ( I x ) of plate about x axis using the formula: I x = 2 ( 1 4 m r 2 + m b 2 ) Substitute 4 kg for m , 180 mm for r , and 150 mm for b . I x = 2 ( 1 4 × 4 ( 180mm× 1m 1000mm ) 2 + 4 ( 150mm× 1m 1000mm ) 2 ) = 0.2448 kg ⋅ m 2 Calculate the moment of inertia ( I y ) of plate about y axis using the formula: I y = 2 ( 1 2 m r 2 + m r 2 ) Substitute 4 kg for m and 180 mm for r . I y = 2 ( 1 2 × 4 ( 180mm × 1m 1000mm ) 2 + 4 ( 180mm × 1m 1000mm ) 2 ) = 0.3888 kg ⋅ m 2 Calculate the moment of inertia ( I z ) of plate about z axis using the formula: I z = 2 ( 1 4 m r 2 + m ( b 2 + r 2 ) ) Substitute 4 kg for m , 180 mm for r , and 150 mm for b . I z = 2 ( 1 4 × 4 ( 180mm× 1m 1000mm ) 2 + 4 [ ( 180m 1000 ) 2 + ( 150 m 1000 ) 2 ] ) = 0.504 kg ⋅ m 2 Calculate the moment of inertia ( I x y ) of plate about xy axis using the formula: I x y = m b ( − r ) + m ( − b ) r = − m b r − m b r = − 2 m b r Substitute 4 kg for m , 180 mm for r , and 150 mm for b . I x y = − 2 × 4 × ( 180mm× 1m 1000mm ) × ( 150mm× 1m 1000mm ) = − 0.216 kg ⋅ m 2 The moment of inertia about xz axis ( I x z ) and yz axis ( I y z ) are zero respectively (b) To determine The angular velocity ( ω ) of the assembly.

Loose Leaf for Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977206

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

Publisher: McGraw-Hill Education

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Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the init…

Question

Chapter 18.1, Problem 18.28P

(a)

To determine

The velocity (v¯) of the mass center G of the assembly.

(b)

To determine

The angular velocity (ω) of the assembly.

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Chapter 18.1, Problem 18.27P

Chapter 18.1, Problem 18.29P

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Chapter 18 Solutions

Loose Leaf for Vector Mechanics for Engineers: Statics and Dynamics

Ch. 18.1 - A thin, homogeneous disk of mass m and radius r...Ch. 18.1 - Prob. 18.2P Ch. 18.1 - Prob. 18.3P Ch. 18.1 - A homogeneous disk of weight W = 6 lb rotates at...Ch. 18.1 - A homogeneous disk of mass m = 8 kg rotates at the...Ch. 18.1 - A solid rectangular parallelepiped of mass m has a...Ch. 18.1 - Prob. 18.8P Ch. 18.1 - Determine the angular momentum HD of the disk of...Ch. 18.1 - Prob. 18.10P Ch. 18.1 - Determine the angular momentum HO of the disk of...

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The velocity ( v ¯ ) of the mass center G of the assembly.

Solution Summary: The author calculates the moment of inertia of plate about x axis using the formula: I_x=2(14m

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The velocity (v¯) of the mass center G of the assembly.

The angular velocity (ω) of the assembly.

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Chapter 18 Solutions