String is wrapped around an object of mass M = 1.1 kg and moment of inertia 1 =

Question

String is wrapped around an object of mass M = 1.1 kg and moment of inertia 1 = 0.04 kgA.m2. You pull the string with your hand straight up with some constant force F such that the center of the object does not move up or down, but the object spins faster and faster (see the figure). This is like a yo-yo; nothing but the vertical string touches the object. when your hand is a height yo = 0.25 m above the floor, the object has an angular speed ?0 = 15 radians/ the angular speed ? of the object? Your answer must be numeric and not contain the symbol F. s. when your hand has risen to a height y = 0.62 m above the floor, what is M,I yo Floor Floor radians/s Additional Materials Section 11.8

Explanation / Answer

by using energy relation,

m*g*(y-yo)=1/2*I*w^2 - 1/2*I*wo^2

1.1*9.8*(0.62-0.25)=1/2*0.04*w^2 -1/2*0.04*15^2

==> W=20.602 rad/sec

angular speed of the object, w=20.602 rad/sec

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