- #1
wingman358
- 18
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Homework Statement
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 "
Homework Equations
M = m g r
ƩM = I α
I = m k^2
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?
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