Acceleration vecloity diagrams relative motion question A l

Acceleration & vecloity diagrams, relative motion question

A light aircraft flies over an observer from A to C as shown (not to scale) in Figure 1. (a) The plane flies at a fixed height of 3 km in a straight line between points A and C, both 3 km away from the observer in the x-direction. At C, the speed of the aircraft is 144 km/h. The plane takes 120 seconds to move from A to C. What is the magnitude and direction of the average angular velocity in rpm of the plane relative to the observer during this time? (b) At point C (v=144 km/h), the plane begins to descend for landing by flying at an angle of 20degree to the horizon as shown in Figure 1. The deceleration of the plane during the descent, is 0.1m/s^2. (i) Draw the velocity components in the r and theta direction and determine r and theta about the observer at this instant. (ii) Calculate the magnitude of r from the observer at this instant. (iii) Calculate the magnitude and direction of the angular acceleration of the plane relative to the observer at this instant.

Solution

A thin-walled closed tube has the cross-section shown. The midline is a circle of radius R. The wall thickness varies linearly with theta from t = t0 at theta = 0 to t = 3t0 at theta = pi. Find the torsional stiffness, T/theta using Bredt\'s formula.