Angular speed of rotating hoop

[henry3369]

Homework Statement

http://imgur.com/jcZRQdu

Homework Equations

The Attempt at a Solution

So I know how to solve this with conservation of energy, but I can't seem to get the correct answer using kinematic equations.

τ_net = Iα = (MR²*(a/R))
-Tension = MRa

F_net = ma
w-Tension = ma
-Tension = ma - mg

Plugging this into the first equation:
ma-mg = MRa
a-g = Ra
a = g/(1-R)
a = 9.8/(1-0.0800) = 10.65 m/s²

v_initial = 0
a = 10.65 m/s²
Δy = 0.45 m
v_final = ?

v_final² = v_initial² + 2aΔy
v_final = sqrt(2aΔy)
v_final = 3.096 m/s
v = rω
ω = v/r = 3.096/0.0800 = 38.7 rad/s

Correct answer: 26.3 rad/s

Again, I know this can be solved with conservation of energy, but I'm trying to figure it out with kinematic equations.

 

[ehild]

Homework Statement

http://imgur.com/jcZRQdu

Homework Equations

What is the question?

What are the relevant equations?

 

[TSny]

τ_net = Iα = (MR²*(a/R))
-Tension = MRa

Dimensional analysis of the second equation above shows that it can't be correct.

 

[henry3369]

What is the question?

What are the relevant equations?

I forgot to include the questions in the picture:
After the hoop has descended 0.45 m, calculate the angular speed of the hoop.

Relevant equations:
τ = Iα
F = ma
Kinematic equations