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Figure 7.12 shows a crude model of a yoyo. A massless
Chapter 7, Problem 7.14(choose chapter or problem)
Figure 7.12 shows a crude model of a yoyo. A massless string is suspended vertically from a fixed point and the other end is wrapped several times around a uniform cylinder of mass m and radius R. When the cylinder is released it moves vertically down, rotating as the string unwinds. Write down the Lagrangian, using the distance x as your generalized coordinate. Find the Lagrange equation of motion and show that the cylinder accelerates downward withi = 2g/3. [Hints: You need to remember from your introductory physics course that the total kinetic energy of a body like the yoyo is T = lmv2 11(02, where v is the velocity of the center of mass, I is the moment of inertia (for a unform cylinder, I = im R2) and co is the angular velocity about the CM. You can express w in terms of I.]
Questions & Answers
QUESTION:
Figure 7.12 shows a crude model of a yoyo. A massless string is suspended vertically from a fixed point and the other end is wrapped several times around a uniform cylinder of mass m and radius R. When the cylinder is released it moves vertically down, rotating as the string unwinds. Write down the Lagrangian, using the distance x as your generalized coordinate. Find the Lagrange equation of motion and show that the cylinder accelerates downward withi = 2g/3. [Hints: You need to remember from your introductory physics course that the total kinetic energy of a body like the yoyo is T = lmv2 11(02, where v is the velocity of the center of mass, I is the moment of inertia (for a unform cylinder, I = im R2) and co is the angular velocity about the CM. You can express w in terms of I.]
ANSWER:Step 1 of 3
The kinetic energy of the system can be given as,
