The 2.3 kg object shown in the figure has a moment of inertia about the rotation axis of 8.9×10−2 kg * m2. The rotation axis is horizontal.
When released, what will be the object’s initial angular acceleration?
Known Variables:
Mass (m): 2.3 kg
Moment of inertia (I): 8.9×10-2 kg * m2
r= 17 cm or .17 m
angle: 25°
gravity: 9.8 m/s2
The force component that causes rotation:
Fg = mg cos(θ)
The torque equation used here is the following:
since, τ = Iα
then,
r x Fg = Iα
solve for α which is angular acceleration:
r x Fg = Iα
α= r x Fg /I
= (.17) x [2.3 kg x 9.8 m/s2 cos(25)] / 8.9 x 10-2kg * m2
= 3.47 / .089
= 38.98
α= 39 rad/s2
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