Question

A 0.2 kg yo-yo consists of two solid disks of radius 5.6 cm joined together by a massless rod of radius 1 cm and a string wrapped around the rod. One end of the string is held fixed and is under constant tension T as the yo-yo is released.

(a) Find the acceleration of the yo-yo

(b) Find the tension T

Answer 1

Answer 2

Solution:

Yo Yo has both translational (linear) as well as rotational motion .

mg -T = ma ----------------(1)

and torque due to rotation = $\tau$ =T r = I $\large \alpha$

I = moment of inertia = 1/2 M R^2 where R = radius of the disks .

Acceleration = $\large \alpha$ = a/r

=>T r = (1/2MR^2)(a/r) , where r = radius of the rod ------------(2)

solve these (1)^(2) to get T & a

a = g / (1+R^2/2r^2) = (9.8) / ( 1+ 0.056² / 2*0.01²) ) = 0. 59 m/s² .

b) Tension = T = m(g-a) = (0.2)(9.8 - 0.59) = 1.84 N