Dynamics_Part63

Dynamics_Part63 - (b) Since the angular velocities of all...

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We observe that gear C is not translating so that v C = 0 , while r E/C = 3 R i . Substituting into the equation relating Points E and C, v E =( ω C k ) × ( 3 R i )= 3 ω C R j Finally, combining the two equations for v E ,wehave 3 ω C R = 1 2 ω A R Therefore, the angular velocity of gear C is ω C = 1 6 ω A Since the magnitude of ω C is negative, gear C rotates clockwise.
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Unformatted text preview: (b) Since the angular velocities of all gears are constant, the accelerations at Point E are purely centrifugal. Therefore, denoting v E = | v E | , a B = v 2 E r E/B = 1 4 2 A R 2 R = 1 4 2 A R a C = v 2 E r E/C = 1 4 2 A R 2 3 R = 1 12 2 A R...
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