This yo-yo's inertia...?

Question

A yo-yo has a rotational inertia of 950 g cm^2 and a mass of 120 g. Its axle radius is 3.2 mm, and its string is 120 cm long. The yo-yo rolls from rest down to the end of the sting.

(a) What is the magnitude of its translational acceleration?

(b) How long does it take to reach the end of the string?

As it reaches the end of the string, what are its (c) translational speed, (d) translational kinetic energy, (e) rotational kinetic energy, and (f) rotational speed?

Explain your work. Thanks! :)

Answer 1

(a)
F= W - T/R
ma=mg - T/R
T=IA
A= a/R we have
ma=mg - I (a/R) /R
ma=mg - I a/R^2
ma + I a/R^2=mg
a= mg/(m + I /R^2)
a=0.120 x 9.81/( 0.120 + 9.50E-5 /(.0032)^2)
a=0.125 m/s^2

b) S=0.5 a t^2
t= sqrt(2S/a)
t= sqrt(2 x 1.20 /0.125)=4.4 s

c )v=0

d) Ke= 0.5 I w^2
You can do the rest....?