Homework Help: Angular speed of rotating hoop

1. Mar 14, 2015

henry3369

1. The problem statement, all variables and given/known data
http://imgur.com/jcZRQdu [Broken]

2. Relevant equations

3. 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.

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

Fnet = 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

vinitial = 0
a = 10.65 m/s2
Δy = 0.45 m
vfinal = ?

vfinal2 = vinitial2 + 2aΔy
vfinal = sqrt(2aΔy)
vfinal = 3.096 m/s
v = rω
ω = v/r = 3.096/0.0800 = 38.7 rad/s

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

Last edited by a moderator: May 7, 2017
2. Mar 14, 2015

ehild

What is the question?

What are the relevant equations?

Last edited by a moderator: May 7, 2017
3. Mar 14, 2015

TSny

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

4. Mar 14, 2015

henry3369

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