An oversized yo-yo is made from two identical solid disks each of massM=2.00kg and radius R=10.0cm. The two disks are joined by a solidcylinder of radius r= 4.00cm and mass m=1.00kg. Take the center of thecylinder as the axis of the system, with positive torques directed tothe left along the axis. All torques and angular variables are to becalculated around this axis. Light string is wrapped around thecylinder, and the system is then allowed to drop from rest. (a) What isthe moment of inertia of the system? Give a symbolic answer. (b) Whattorque does gravity exert on the system with respect to the givenaxis. (c) Take downward as the negative coordinate direction. Is theangular acceleration positive or negative? What about the translationalacceleration? (d) we an equation for the angular acceleration(alpha) in terms of the translation acceleration a and radius r. (e)Write Newton's second law for the system in terms of m, M, a,T, and g. (f) Write Newton's second law for rotation in terms of I, alpha, T, andr. (g) Eliminate alpha from the rotational second law with theexpression found in part (d) and find a symbolic expression for theacceleration a in terms of m, M, g, r, and R. (h) What is the numericvalue for the system's acceleration? (i) What is the tension in thestring? (j) How long does it take the system to drop 1.00m from rest?
An oversized yo-yo is made from two identical solid disks each of massM=2.00kg and radius R=10.0cm. The two disks are joined by a solidcylinder of radius r= 4.00cm and mass m=1.00kg. Take the center of thecylinder as the axis of the system, with positive torques directed tothe left along the axis. All torques and angular variables are to becalculated around this axis. Light string is wrapped around thecylinder, and the system is then allowed to drop from rest. (a) What isthe moment of inertia of the system? Give a symbolic answer. (b) Whattorque does gravity exert on the system with respect to the givenaxis. (c) Take downward as the negative coordinate direction. Is theangular acceleration positive or negative? What about the translationalacceleration? (d) we an equation for the angular acceleration(alpha) in terms of the translation acceleration a and radius r. (e)Write Newton's second law for the system in terms of m, M, a,T, and g. (f) Write Newton's second law for rotation in terms of I, alpha, T, andr. (g) Eliminate alpha from the rotational second law with theexpression found in part (d) and find a symbolic expression for theacceleration a in terms of m, M, g, r, and R. (h) What is the numericvalue for the system's acceleration? (i) What is the tension in thestring? (j) How long does it take the system to drop 1.00m from rest?
