Explanation Given information: Acceleration of the body is a _ _ . Angular velocity of the body is ω . Angular acceleration of the body is α . Position vector of particle P i is r i . Calculation: Acceleration of P i , a i = a _ _ + a i G a i = a _ _ + α r i + ω × ( ( − ω ) r i ) a i = a _ _ + α r i − ω 2 r i Effective force on the body, F = Δ m i a i F = Δ m i ( a _ _ + α r i − ω 2 r i ) F = Δ m i a _ _ + Δ m i α r i - Δ m i ω 2 r i Force consist of the terms, Δ m i a _ _ , Δ m i α r i a n d - Δ m i ω 2 r i . Total mass of the rigid body is the summation of small masses. ∑ Δ m i = m . G is the mass center of the body, ∑ Δ m i r i = m r i _ _ . So, ∑ Δ m i a i = m a _ _

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Chapter 16.1, Problem 16.47P

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To show: The system terms consist of vectors (△mi)a, −(△mi)ω2ri,,and (△mi)(α×ri,).

To show: The inertial terms reduce to a vector ma attached at G and a couple I¯α.

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Chapter 16.1, Problem 16.46P

Chapter 16.1, Problem 16.48P

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The system terms consist of vectors ( △ m i ) a _ _ , − ( △ m i ) ω 2 r i , , a n d ( △ m i ) ( α × r i , ) . To show: The inertial terms reduce to a vector m a _ _ attached at G and a couple I ¯ α .

Solution Summary: The author explains how the inertial terms reduce to a vector mstackrel_a attached at G.

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To show: The system terms consist of vectors (△mi)a, −(△mi)ω2ri,,and (△mi)(α×ri,).

To show: The inertial terms reduce to a vector ma attached at G and a couple I¯α.

Want to see the full answer?

Chapter 16 Solutions

The system terms consist of vectors ( △ m i ) a _ _ , − ( △ m i ) ω 2 r i , , a n d ( △ m i ) ( α × r i , ) . To show: The inertial terms reduce to a vector m a _ _ attached at G and a couple I ¯ α .

Solution Summary: The author explains how the inertial terms reduce to a vector mstackrel_a attached at G.

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To show: The system terms consist of vectors (△mi)a__, −(△mi)ω2ri,,and (△mi)(α×ri,). To show: The inertial terms reduce to a vector ma__ attached at G and a couple I¯α.

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Chapter 16 Solutions

To show: The system terms consist of vectors (△mi)a, −(△mi)ω2ri,,and (△mi)(α×ri,).

To show: The inertial terms reduce to a vector ma attached at G and a couple I¯α.