Problem

The Pioneer 3 spacecraft was a spin-stabilized spacecraft launched on December 6, 1958, by...

The Pioneer 3 spacecraft was a spin-stabilized spacecraft launched on December 6, 1958, by the U.S. Army Ballistic Missile agency in conjunction with NASA. It was designed with a despin mechanism consisting of two equal masses A and B that could be spooled out to the end of two wires of variable length ℓ(t) when triggered by a hydraulic timer. As a prelude to Probs. 7.64, 7.65, and 8.77, we will find the velocityand acceleration of each the two masses. To do this, assume that masses A and B are initially at positions A0 and B0, respectively. After the masses are released, they begin to unwind symmetrically, and the length of the cord attaching each mass to the spacecraft of radius R is ℓ(t). Given that the angular velocity of the spacecraft at each instant is ωs(t), determine

(a) The velocity of mass A

(b) The acceleration of mass A

in components expressed in the rotating reference frame whose origin is at Q, as well as R, ℓ(t), and ωs(t). Note that the rotating frame is always aligned with the unwinding cord, and Q is the point on the cord that is about to unwind at time t.