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for the primitive yo-yo in fig, to find the downward acceleration of the cylinder and the tension in the string. you can take the toy as solid cylinder and icm=1/2mr2 , where m is the mass of the yo-yo toy

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onyebuchinnaji

The downward acceleration of the solid cylinder at the given tension in the string is determined as 2Tr/MR.

Downward acceleration of the cylinder

The downward acceleration of the solid cylinder is determined from the principle of conservation of angular momentum as shown below;

Iα = Tr

where;

  • I is moment of inertia of the solid cylinder
  • α is angular acceleration of the cylinder
  • T is tension in the string
  • r is length of the string

α = Tr/I

[tex]\frac{a}{R} = \frac{Tr}{I} \\\\\frac{a}{R} = \frac{Tr}{\frac{1}{2} MR^2}\\\\\frac{a}{R} =\frac{2Tr}{MR^2} \\\\a = \frac{2Tr}{MR}[/tex]

where;

  • a is the downward acceleration of the solid cylinder
  • R is radius of the cylinder

Thus, the downward acceleration of the solid cylinder at the given tension in the string is determined as 2Tr/MR.

Learn more about acceleration here: https://brainly.com/question/605631

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