An oversized yo-yo is made from two identical solid disks each of mass M = 1.60

Question

An oversized yo-yo is made from two identical solid disks each of mass M = 1.60 kg and radius R = 9.7 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, with positive torques directed to the left along this axis. All torques and angular variables are to be calculated around this axis. Light string is wrapped around the cylinder, and the system is then allowed to drop from rest. (b) What torque does gravity exert on the system with respect to the given axis? (g) Eliminate ? from the rotational second law with the expression found in part (d) and find a symbolic expression for the acceleration a in terms of m, M, g, r and R. (h) What is the numeric value for the system's acceleration? (i) What is the tension in the string? (j) How long does it take the system to drop 1.00 m from rest?

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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