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656_Dynamics 11ed Manual

# 656_Dynamics 11ed Manual - velocity just before the collar...

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Engineering Mechanics - Dynamics Chapter 19 Problem 19-37 Each of the two slender rods and the disk have the same mass m . Also, the length of each rod is equal to the diameter d of the disk. If the assembly is rotating with an angular velocity ω 1 when the rods are directed outward, determine the angular velocity of the assembly if by internal means the rods are brought to an upright vertical position. Solution: H 1 H 2 = 1 2 m d 2 2 2 1 12 md 2 + 2 md 2 + 1 1 2 m d 2 2 2 m d 2 2 + 2 = 2 11 3 1 = Problem 19-38 The rod has a length L and mass m . A smooth collar having a negligible size and one-fourth the mass of the rod is placed on the rod at its midpoint. If the rod is freely rotating with angular velocity about its end and the collar is released, determine the rod’s angular
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Unformatted text preview: velocity just before the collar flies off the rod. Also, what is the speed of the collar as it leaves the rod? Solution: H 1 H 2 = 1 3 mL 2 m 4 ⎛ ⎝ ⎞ ⎠ L 2 ⎛ ⎝ ⎞ ⎠ L 2 ⎛ ⎝ ⎞ ⎠ + 1 3 mL 2 ' m 4 ⎛ ⎝ ⎞ ⎠ L ' L + = ' 19 28 = T 1 V 1 + T 2 V 2 + = 1 2 1 3 mL 2 ⎛ ⎝ ⎞ ⎠ 2 1 2 m 4 ⎛ ⎝ ⎞ ⎠ L 2 ⎛ ⎝ ⎞ ⎠ 2 + 1 2 m 4 ⎛ ⎝ ⎞ ⎠ v' 2 1 2 m 4 ⎛ ⎝ ⎞ ⎠ L ' ( ) 2 + 1 2 1 3 mL 2 ⎛ ⎝ ⎞ ⎠ ' 2 + = v' 2 57 112 L 2 2 = v'' 0.985 L = v'' 57 112 L 2 2 L 19 28 ⎛ ⎝ ⎞ ⎠ ⎡ ⎣ ⎤ ⎦ 2 + = v'' 95 98 L = 654...
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