Yoyo The figure below shows a crude model of a yoyo. A massless string 4. suspended vertically from a fixed point and the other end 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 with 2q/3. wrapped several times 1 Hints: You need to remember from your introductory physics course that the total kinetic energy of a body like the yoyo is T = mu Iw, where v is the velocity of the center of mass, I is the moment of inertia (for a uniform cylinder, I =mR2) and w is the angular velocity about the CM. You can express w in terms of å.] x R

Question
Yoyo The figure below shows a crude model of a yoyo. A massless string
4.
suspended vertically from a fixed point and the other end
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 with 2q/3.
wrapped several times
1
Hints: You need to remember from your introductory physics course that the total
kinetic energy of a body like the yoyo is T = mu Iw, where v is the velocity of
the center of mass, I is the moment of inertia (for a uniform cylinder, I =mR2) and
w is the angular velocity about the CM. You can express w in terms of å.]
x
R
Expand
Transcribed Image Text

Yoyo The figure below shows a crude model of a yoyo. A massless string 4. suspended vertically from a fixed point and the other end 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 with 2q/3. wrapped several times 1 Hints: You need to remember from your introductory physics course that the total kinetic energy of a body like the yoyo is T = mu Iw, where v is the velocity of the center of mass, I is the moment of inertia (for a uniform cylinder, I =mR2) and w is the angular velocity about the CM. You can express w in terms of å.] x R

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