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3) A yo-yo of mass 200g and diameter 5 cm rolls down a thread without slipping for 1 m and spins at the bottom. For this problem consider the yo-yo to be made of two (equal in all ways) disks joined together at its centers with an axel of negligible mass, length and thickness. What is its angular velocity when it comes down fully?

Respuesta :

Answer:

[tex]\omega=177.09\ rad.s^{-1}[/tex]

Explanation:

Given :

  • mass of yo-yo, [tex]m=0.2\ kg[/tex]
  • radius of yo-yo, [tex]r=0.025\ m[/tex]
  • distance of descend of yo-yo, [tex]h=1\ m[/tex]

Linear velocity of yo-yo at the bottom:

[tex]v^2=u^2+2g.h[/tex]

[tex]v^2=0^2+2\times 9.8\times 1[/tex]

[tex]v=4.4272\ m.s^{-1}[/tex]

Now using the relation between angular and linear velocity:

[tex]\omega=\frac{v}{r}[/tex]

[tex]\omega=\frac{4.4272}{0.025}[/tex]

[tex]\omega=177.09\ rad.s^{-1}[/tex]

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