Question

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.

Answer 1

Answer:

linear acceleration

$a = \frac{2g}{2 + \frac{R}{b}}$

angular acceleration

$\alpha = \frac{2g}{R(2 + \frac{R}{b})}$

Explanation:

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

so we will have

$2mg - T = 2ma$

also we have

$Tb = (\frac{1}{2}mR^2 + \frac{1}{2}mR^2)\alpha$

now we have

$Tb = mR^2(\frac{a}{R})$

$T = \frac{mRa}{b}$

now we have

$2mg = (2ma + \frac{mRa}{b})$

$a(2 + \frac{R}{b}) = 2g$

so we have

linear acceleration

$a = \frac{2g}{2 + \frac{R}{b}}$

angular acceleration

$\alpha = \frac{2g}{R(2 + \frac{R}{b})}$