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
     v_B = r_B ω
     60 = 2 ω
     ω = 30 rad/s

Angular Acceleration
     a_Bt = r_B α
     400 = 2 α
     α = 200 rad/s²

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

     a_An = ω²r_A
           = 900 (1.5) = 1,350 ft/s²

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

A = 1,383 ft/s²