Let's consider a 1970's style record player, with a record on it. The turntable is rotating at a con- stant counterclock

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Let S Consider A 1970 S Style Record Player With A Record On It The Turntable Is Rotating At A Con Stant Counterclock 1 (56.06 KiB) Viewed 67 times

Let's consider a 1970's style record player, with a record on it. The turntable is rotating at a con- stant counterclockwise (as seen from the top) speed of 33 1/3 rpm. An ant is also sitting on the record, 4in from the center in the position shown. At the instant shown, the ant begins walking radially, toward the center of the record at a rate of 2in/min. Two frames are shown: Vo = {0;ex} is the fixed frame, and th = {0; ek} rotates with the turntable. ez, e Ant Te ez e e Question 1 What is the direction cosine matrix, relating these two reference frames? SU Question 2 At the instant in question, what is the translational velocity of the ant in the fixed frame, referred to the rotating frame? Use our general derivative expression for rotating frames: 0 4 + wyxU. Express your answers in the units: in/min. Question 3 As an alternative, convert the position vector out of the primed unit vectors and into the unprimed, and then take derivatives. This will, in a sense, make life easier because the derivatives of the tho (unprimed) unit vectors are zero. But the expressions will be a bit uglier - even though they represent the same vector. Why does the angle o show up in this expression?