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An oversized yo-yo is made from two identical solid disks each of mass N- 1.60 kg and radius R 9.0 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 syste (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 - MR +m (b) What torque does gravity exert on the system with respect to the given axds? v Nm 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 counterdockwise direction be positive.) positive O negative (d) Is the angular acceleration positive or negative? positive O negative (e) What about the translational acceleration? O positive negative () Write an equation for the angular acceleration a (alpha) terms of the translational acceleration a and radius r. (Watch the signl) (9) Write Newton's second laaw for the system in terms of m, M, a, T, and g. (De this on paper. Your instructor may ask you to turn in this work.) (h) Write Newton's second law for rotation in terms of 1, a, T, and r. (Do this on paper. Your instructor may ask you to turn in this work.) (1) Eliminate a from the rotational second law with the expression found in part () and find a symbolic expression for the acceleration a in terms of m, M, g, rand R. 0) What is the numeric value for the system's acceleration? The correct answer is not zero. mys (k) What is the tension in the string? The correct answer is not zero. N m Hew longn does it take the system to drop 0.80 m from rest?

An oversized yo-yo is made from two identical solid disks each of mass N- 1.60 kg and radius R 9.0 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 syste (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 - MR +m (b) What torque does gravity exert on the system with respect to the given axds? v Nm 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 counterdockwise direction be positive.) positive O negative (d) Is the angular acceleration positive or negative? positive O negative (e) What about the translational acceleration? O positive negative () Write an equation for the angular acceleration a (alpha) terms of the translational acceleration a and radius r. (Watch the signl) (9) Write Newton's second laaw for the system in terms of m, M, a, T, and g. (De this on paper. Your instructor may ask you to turn in this work.) (h) Write Newton's second law for rotation in terms of 1, a, T, and r. (Do this on paper. Your instructor may ask you to turn in this work.) (1) Eliminate a from the rotational second law with the expression found in part () and find a symbolic expression for the acceleration a in terms of m, M, g, rand R. 0) What is the numeric value for the system's acceleration? The correct answer is not zero. mys (k) What is the tension in the string? The correct answer is not zero. N m Hew longn does it take the system to drop 0.80 m from rest?

International Edition---engineering Mechanics: Statics, 4th Edition
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter9: Moments And Products Of Inertia Of Areas
Section: Chapter Questions
Problem 9.87RP
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An oversized yo-yo is made from two identical solid disks each of mass M - 1.60 kg and radius R- 9.0 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- MR + (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 countercdockwise direction be positive.) 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 () 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 terms of I, a, T, and r. (Do this on paper. Your instructor may ask you to turn in this work.) (1) Eliminate a from the rotational second law with the expression found in part () and find a symbolic expression for the acceleration a in terms of m, M, g, rand R. () What is the numeric value for the system's acceleration? The correct answer is not zero. m/s (k) What is the tension in the string? The correct answer is not zero. N (1) How long does it take the system to drop 0.80 m from rest? The correct answer is not zero. s
Transcribed Image Text:An oversized yo-yo is made from two identical solid disks each of mass M - 1.60 kg and radius R- 9.0 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- MR + (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 countercdockwise direction be positive.) 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 () 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 terms of I, a, T, and r. (Do this on paper. Your instructor may ask you to turn in this work.) (1) Eliminate a from the rotational second law with the expression found in part () and find a symbolic expression for the acceleration a in terms of m, M, g, rand R. () What is the numeric value for the system's acceleration? The correct answer is not zero. m/s (k) What is the tension in the string? The correct answer is not zero. N (1) How long does it take the system to drop 0.80 m from rest? The correct answer is not zero. s
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