674_Dynamics 11ed Manual

674_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 20 Given: ω1 = 3 rad s ω2 = 1.5 ω'1 = 2 rad ω'2 = 4 2 s θ 1 = 30 deg rad s rad 2 s d = 3 ft Solution: ⎛ ω2 ⎞ ⎜⎟ ω=⎜0⎟ ⎜ω ⎟ ⎝ 1⎠ ⎛ ω'2 ⎞ ⎛ 0 ⎞ ⎜ ⎟⎜⎟ α = ⎜ 0 ⎟+⎜ 0 ⎟×ω ⎜ ω' ⎟ ⎜ ω1 ⎟ ⎝ 1⎠ ⎝ ⎠ ⎛0 ⎞ ⎜ ⎟ rA = ⎜ d cos ( θ 1 ) ⎟ ⎜ d sin ( θ ) ⎟ 1⎠ ⎝ vA = ω × rA ⎛ −7.79 ⎞ ⎜ ⎟ ft vA = −2.25 ⎜ ⎟s ⎝ 3.90 ⎠ vA = 9 aA = α × rA + ω × ( ω × rA) ⎛ 8.30 ⎞ ⎜ ⎟ ft aA = −35.23 ⎜ ⎟2 ⎝ 7.02 ⎠ s aA = 36.868 *Problem 20-8 The cone rolls without slipping such that at the instant shown ωz and ω'z are as given. Determine the velocity and acceleration of point A at this instant. Given: ωz = 4 rad s ω'z = 3 rad 2 s 672 ft s ft 2 s ...
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