A 0.2 kg yo-yo consists of two solid disks of radius 5.5 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.

Question

a. Find the acceleration of the yo-yo.

b. Find the tension T.

Answer 1

Given:
m=0.2
R=5.5
r=1

l = 0.5*mR^2
=(0.5*0.2*5.5^2)
=3.025

a. a=g[1 - I/(mr^2 + I)]
=9.8[1 - (0.5*0.2*5.5^2)/(0.2*1^2 + (0.5*0.2*5.5^2))]
=0.61 m/s^2

b. T=g/[r^2/I + 1/m]
=9.8/[1^2/(0.5*0.2*5.5^2) + 1/0.2]
=1.84 N