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An oversized yo-yo is made from two identical solid disks each of mass M = 2.00 kg and radius R = 10.0 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. (a) What is the moment of inertia of the system? Give a symbolic answer. (Use any variable or symbol stated above as necessary.) moment of inertia =| 0.5(mr2 + 2MR2) (b) What torque does gravity exert on the system with respect to the given axis? V N•m Take downward as the negative coordinate direction. (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.) O positive O negative (d) Is the angular acceleration positive or negative? O positive O negative (e) What about the translational acceleration? lo positive O negative (f) Write an equation for the angular acceleration a (alpha) in terms of the translational acceleration a and radius r. (Watch the sign!) (9) 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.) (h) Write Newton's second law for rotation in terms of I, a, T, and r. (Do this on paper. Your instructor may ask you to turn in this work.) (i) Eliminate a 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. ( 2M + m) g + 1.5m a =

An oversized yo-yo is made from two identical solid disks each of mass M = 2.00 kg and radius R = 10.0 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. (a) What is the moment of inertia of the system? Give a symbolic answer. (Use any variable or symbol stated above as necessary.) moment of inertia =| 0.5(mr2 + 2MR2) (b) What torque does gravity exert on the system with respect to the given axis? V N•m Take downward as the negative coordinate direction. (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.) O positive O negative (d) Is the angular acceleration positive or negative? O positive O negative (e) What about the translational acceleration? lo positive O negative (f) Write an equation for the angular acceleration a (alpha) in terms of the translational acceleration a and radius r. (Watch the sign!) (9) 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.) (h) Write Newton's second law for rotation in terms of I, a, T, and r. (Do this on paper. Your instructor may ask you to turn in this work.) (i) Eliminate a 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. ( 2M + m) g + 1.5m a =

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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An oversized yo-yo is made from two identical solid disks each of mass M = 2.00 kg and radius R = 10.0 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. 00 (a) What is the moment of inertia of the system? Give a symbolic answer. (Use any variable or symbol stated above as necessary.) 0.5 (mr² + 2MR²) moment of inertia = (b) What torque does gravity exert on the system with respect to the given axis? N•m Take downward as the negative coordinate direction. (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.) O positive O negative (d) Is the angular acceleration positive or negative? O positive O negative (e) What about the translational acceleration? O positive O negative (f) Write an equation for the angular acceleration a (alpha) in terms of the translational acceleration a and radius r. (Watch the sign!) = (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.) (h) Write Newton's second law for rotation in terms of I, a, T, and r. (Do this on paper. Your instructor may ask you to turn in this work.) (i) Eliminate a 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. ( 2M + m) g +1.5m R² a = M2 + (j) What is the numeric value for the system's acceleration? -2.14 Your response differs from the correct answer by more than 10%. Double check your calculations. m/s (k) What is the tension in the string? 41.801 Your response differs from the correct answer by more than 10%. Double check your calculations. N (1) How long does it take the system to drop 1.00 m from rest? (0.6925 Your response differs from the correct answer by more than 10%. Double check your calculations. s
Transcribed Image Text:An oversized yo-yo is made from two identical solid disks each of mass M = 2.00 kg and radius R = 10.0 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. 00 (a) What is the moment of inertia of the system? Give a symbolic answer. (Use any variable or symbol stated above as necessary.) 0.5 (mr² + 2MR²) moment of inertia = (b) What torque does gravity exert on the system with respect to the given axis? N•m Take downward as the negative coordinate direction. (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.) O positive O negative (d) Is the angular acceleration positive or negative? O positive O negative (e) What about the translational acceleration? O positive O negative (f) Write an equation for the angular acceleration a (alpha) in terms of the translational acceleration a and radius r. (Watch the sign!) = (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.) (h) Write Newton's second law for rotation in terms of I, a, T, and r. (Do this on paper. Your instructor may ask you to turn in this work.) (i) Eliminate a 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. ( 2M + m) g +1.5m R² a = M2 + (j) What is the numeric value for the system's acceleration? -2.14 Your response differs from the correct answer by more than 10%. Double check your calculations. m/s (k) What is the tension in the string? 41.801 Your response differs from the correct answer by more than 10%. Double check your calculations. N (1) How long does it take the system to drop 1.00 m from rest? (0.6925 Your response differs from the correct answer by more than 10%. Double check your calculations. s
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