<p>An oversized yo-yo is made from two identical solid disks each of mass M = 1.

Question

<p>An oversized yo-yo is made from two identical solid disks each of mass M = 1.60 kg and radius R = 11.5 cm. The two disks are joined by a solid cylinder of radius r = 4.00 cm and mass m = 1.00 kg as in the figure below. Take the center of the cylinder as the axis of the system.<br />(a) What is the moment of inertia of the system? Give a symbolic answer. (Use any variable or symbol stated above as necessary.)<br />moment of inertia = Your answer is incorrect.<br /><br /><br />(b) What torque does gravity exert on the system with respect to the given axis?<br />Your answer is correct. N&#183;m<br /><br />Take downward as the negative coordinate direction.<br />(c) As depicted in the figure above, is the torque exerted by the tension positive or negative? (View the yo-yo from the left and let the counterclockwise direction be positive.)<br /><br />positive negative Your answer is correct.<br /><br />(d) Is the angular acceleration positive or negative?<br /><br />positive negative Your answer is correct.<br /><br />(e) What about the translational acceleration?<br /><br />positive negative Your answer is correct.<br /><br />(f) Write an equation for the angular acceleration &#945; (alpha) in terms of the translational acceleration a and radius r. (Watch the sign!)<br />&#945; = Your answer is incorrect.<br /><br /><br />(g) Write Newton's second law for the system in terms of m, M, a, T, and g. (Do this on paper. Your instructor may ask you to turn in this work.)<br /><br />(h) Write Newton's second law for rotation in terms of I, &#945;, T, and r. (Do this on paper. Your instructor may ask you to turn in this work.)<br /><br />(i) Eliminate &#945; from the rotational second law with the expression found in part (f) and find a symbolic expression for the acceleration a in terms of m, M, g, r and R.<br />a = <br /><br /><br />(j) What is the numeric value for the system's acceleration?<br />&#160;m/s2<br /><br />(k) What is the tension in the string?<br />N<br /><br />(l) How long does it take the system to drop 1.10 m from rest?<br />s</p>

Explanation / Answer

R = 0.094 mr = 0.04 mFirst find the moment of inertia of the yo-yo:I = ?I = 2 x (1/2)MR2 + (1/2)mr2 =MR2 + mr2? = r FThe force is just the weight of the yo-yo? = r(M + m)Newton's second law for rotating bodies? = I ?r(M + m) = (MR2 + mr2)?Solve for ?.a = r? will give the translational acceleration.

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