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A yo-yo is made from two uniform disks, each with mass m and radius R, connected by a light axle of radius b. A light, thin string is wound several times around the axle and then held stationary while the yo-yo is released from rest, dropping as the string unwinds. Find the linear acceleration and angular acceleration of the yo-yo and the tension in the string.

Respuesta :

Answer:

linear acceleration

[tex]a = \frac{2g}{2 + \frac{R}{b}}[/tex]

angular acceleration

[tex]\alpha = \frac{2g}{R(2 + \frac{R}{b})}[/tex]

Explanation:

As we know that the force due to tension force is upwards while weight of the disc is downwards

so we will have

[tex]2mg - T = 2ma[/tex]

also we have

[tex]Tb = (\frac{1}{2}mR^2 + \frac{1}{2}mR^2)\alpha[/tex]

now we have

[tex]Tb = mR^2(\frac{a}{R})[/tex]

[tex]T = \frac{mRa}{b}[/tex]

now we have

[tex]2mg = (2ma + \frac{mRa}{b})[/tex]

[tex]a(2 + \frac{R}{b}) = 2g[/tex]

so we have

linear acceleration

[tex]a = \frac{2g}{2 + \frac{R}{b}}[/tex]

angular acceleration

[tex]\alpha = \frac{2g}{R(2 + \frac{R}{b})}[/tex]

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