tube is hinged to a rotating base as shown in Fig. 4. At the instant shown, the base rotates
about the z axis with a constant angular velocity ! 1 = 2 rad/s. At the same instant, the
2

 

 

tube rotates upward from the base at a constant rate ! 2 = 5 rad/s. Moreover, the ball B is
blowing through the tube at a constant velocity. Note that coordinates xyz are attached to
the rotating base. Answer the following question.
(a) What is the angular velocity ~! a of the xyz frame? Express ~! a in a vector form.
(b) What is the angular velocity ~! of the tube? Express ~! in a vector form.
(c) What is the angular acceleration ~↵ of the tube? Express ~↵ in a vector form.
(d) In this xyz coordinate system, the relative velocity of the ball to the tube is given as
7j + 15k. What is the Coriolis acceleration in its vector form? [Hint: Use relative
motion in rotating frames.]
(e) What is the velocity of the tip of the tube, if the length of the tube is 5 m?

N w = 2 rad/s W2 = 5 rad/s F=3m 9 = 30F y Figure 4: A ball moving through a rotat- ing tube