p0710 - v B = R j + R w 2 j 1 2 i W = 1 2 R i + ( 2 ) R j...

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7.10. CHAPTER 7, PROBLEM 10 315 7.10 Chapter 7, Problem 10 Problem: Ad i sko fr ad iu s R is mounted on L-shaped Rod CD and rotates with constant angular velocity ω as shown. Rod CD rotates with constant angular velocity about the z axis. Determine the absolute velocity and acceleration of Point B, which is the lowest point on the disk relative to the xy plane. Solution: An observer in a coordinate frame rotating with angular velocity = k about Point D sees the motion of Point B as pure rotation with angular velocity ω = ω i about the center of the disk (Point C). Thus, the relative velocity and acceleration vectors are v I B = ω × r B/C = ω i × ( R k )= ω R j a I B = ω × v I B = ω i × ω R j = ω 2 R k The absolute velocity of Point B is given by v B = v I B + × r B/D where r B/D is given by r B/D = 2 R i + 1 2 R j R
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Unformatted text preview: v B = R j + R w 2 j 1 2 i W = 1 2 R i + ( 2 ) R j Point Bs absolute acceleration is a B = a I B + r B/D + 2 v I B + ( r B/D ) where v I B is the collars velocity as seen by the rotating observer and r B/D is its position vector relative to the collar. Now, we know that = , while v I B and a I B are as given above. Thus, the absolute acceleration of Point B is a B = 2 R k + 2 k R j + k } k w 2 R i + 1 2 R j R k W] = 2 R k 2 R i + k } R w 2 j 1 2 i W] = 2 R k 2 R i + 2 R } 2 i 1 2 j ] = 2( ) R i 1 2 2 R j + 2 R k...
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