lec03 - Example 2 Particle on String Pulled Through Hole 1...

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Cite as: Thomas Peacock and Nicolas Hadjiconstnatinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 1 Example 2: Particle on String Pulled Through Hole 2.003J/1.053J Dynamics and Control I, Spring 2007 Professor Thomas Peacock 2/14/2007 Lecture 3 Dynamics of a Single Particle: Angular Momentum Example 2: Particle on String Pulled Through Hole Figure 1: Particle on string pulled through hole. Tabletop with hole B. A string comes out with an attached mass. The particle is traveling around with an angular velocity θ ˙ . Figure by MIT OCW. Assume: Frictionless surface. Inextensible String. Pull string through hole at B such that: dr r ( t 0 ) = L dt ( t 0 ) = 0 r ( t 1 ) = L/ 2 dr ( t 1 ) = 0 dt If θ ˙ ( t 0 ) = θ ˙ 0 , what is θ ˙ ( t 1 ) = θ ˙ 1 ?
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Cite as: Thomas Peacock and Nicolas Hadjiconstnatinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 2 Dynamics of systems of particles Discussion If we use linear momentum, will need to describe forces between m and string. Thinking about angular momentum about the point B: τ B = h ˙ B + v B × mv Angular momentum principle h B = r × mv = Angular Momentum Now: τ B = r × F Forces acting on particle τ B = 0 because r F τ B = h ˙ B + v B × mv Angular momentum
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