9-j4 A book is spinning around a circle of radius R on top of a flat tabletop. T

Question

9-j4 A book is spinning around a circle of radius R on top of a flat tabletop. The speed of the book is initially vo. The inward force is provided by a string attached to the book, going through a hole at the center of the circle (r = 0), and passing underneath to a person holding the string. The person pulls on the string so that the book spirals inward, eventually cutting the radius of the circular motion in half (a) what is the speed of the book at r = R/2? (b) How much work is done by the person pulling

Explanation / Answer

Conserving angular momentum

M*v*R=M*v'*R/2

We got

v'=2v

Work done =change in kinetic energy=0.5*m*(4-1)*v*v=1.5mv*v

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