Angular Acceleration of a Pulley Supporting Two Hanging Masses

1. Apr 28, 2012

wingman358

1. The problem statement, all variables and given/known data

Hi all! I'm working on a dynamics homework and have hit a wall here:

"If the frictional moment at the pivot O is 2 N m, determine the angular acceleration of the grooved drum, which has a mass of 8 kg and a radius of gyration k = 225 mm.

Ans: α = 0.622 rad/s^2 "

2. Relevant equations

M = m g r

ƩM = I α

I = m k^2

3. The attempt at a solution

The two masses exert moments about O, so my first step is to sum the moments about the pivot O:

ƩM = (12 kg)(9.81 m/s^2)(0.2 m) - (7 kg)(9.81 m/s^2)(0.3 m)
ƩM = 2.943 N m

These moments are resisted by the frictional moment such that:

ƩM = (2.943 N m) - (2 N m)
ƩM = 0.943 N m

Next we need the moment of inertia of the pulley:

I = m_pulley * k^2
I = (8 kg)(0.225 m)^2
I = 0.405 kg m^2

Finally we can solve for angular acceleration:

ƩM = I α
so
α = ƩM / I
α = (0.943 N m) / (0.405 kg m^2)
α = 2.33 1 / s^2

My analysis seems reasonable and I come up with the right units, but it is not very close to the given answer.

Am I doing something wrong?

Last edited: Apr 28, 2012