Rotating Bracket


A angled bracket rotates about a fixed shaft O. If the tangential acceleration and velocity of point B is 400 ft/s2 and 60 ft/s, respectively, what is the total acceleration magnitude of point A?


Angular Velocity and Acceleration


This problem is a basic fixed-axis rotation problem since the problem explicitly states there is a fixed shaft. First, determine the angular velocity and angular acceleration.

Angular Velocity
     vB = rB ω
     60 = 2 ω
     ω = 30 rad/s

Angular Acceleration
     aBt = rB α
     400 = 2 α
     α = 200 rad/s2

Use ω and α to find normal and tangent acceleration of point A
     aAt = rA α
           = (1.5)(200) = 300 ft/s2

     aAn = ω2rA
           = 900 (1.5) = 1,350 ft/s2

Total Acceleration
     aA = (1,3502 + 3002)0.5 = 1,383 ft/s2

A = 1,383 ft/s2

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