An oversized yo-yo is made from two identical solid disks each ofmass M=2.00kg and radius R=10.0 cm. The two disks are joined by asolid bylinder of radius r=4 cm and mass m=1 kg. Take the center ofthe bylinder as the axis of the system, with positive torquesdirected to the left along this axis. Light string is wrappedaround the cylinder, and the system is then allowed to drop fromrest.
a. what is the moment of inertia? Give a symbolic answer b. whattorque does gravity exert on the system with respect to the fivenaxis? c. Take downward as negative coordinate direction. Is torqueexerted by the tension positive or negative? what about thetranslational acceleration? d. What is an equation for the angularacceleration in terms of translational 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,angular acceleration, T and r. G. Elimintate rotational second lawfound i part d and find a symbolic expression for the accelerationain terms of m, M, g, r and R. h. What is the numerica value for thesystem's acceleration? I. What is the tension in the string? J. Howlong does it take the system to drop 1.oom from rest?
An oversized yo-yo is made from two identical solid disks each ofmass M=2.00kg and radius R=10.0 cm. The two disks are joined by asolid bylinder of radius r=4 cm and mass m=1 kg. Take the center ofthe bylinder as the axis of the system, with positive torquesdirected to the left along this axis. Light string is wrappedaround the cylinder, and the system is then allowed to drop fromrest.
a. what is the moment of inertia? Give a symbolic answer b. whattorque does gravity exert on the system with respect to the fivenaxis? c. Take downward as negative coordinate direction. Is torqueexerted by the tension positive or negative? what about thetranslational acceleration? d. What is an equation for the angularacceleration in terms of translational 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,angular acceleration, T and r. G. Elimintate rotational second lawfound i part d and find a symbolic expression for the accelerationain terms of m, M, g, r and R. h. What is the numerica value for thesystem's acceleration? I. What is the tension in the string? J. Howlong does it take the system to drop 1.oom from rest?
