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songoku
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Homework Statement
A rod with one end fixed on a smooth hinge is shown below.
The rod is released from horizontal position so that it rotates at the hinge. The mass of the rod is 800 gr and the length is 120 cm. Find:
a. the initial angular acceleration (at A)
b. the angular acceleration at B
c. angular speed at B
d. the speed of the edge of the rod at B
Homework Equations
KE rotation = 1/2 Iω2
KE translation = 1/2 mv2
PE = mgh
τ = I.α
τ = F.d
The Attempt at a Solution
The moment of inertia will be 1/3 ML2
a.
τ = I.α
F.d = 1/3 ML2.α
8 x 0.6 = 1/3 x 0.8 x (1.2)2 x α
α = 12.5 rad/s2
b.
τ = I.α
8 x 0.6 sin 37° = 1/3 x 0.8 x (1.2)2 x α
α = 7.52 rad/s2
c. don't know
d. My idea is using conservation of energy; the decrease of potential energy of the center of mass = the gain of rotational kinetic energy and translational kinetic energy
m.g.1/2 L cos 37° = 1/2 Iω2 + 1/2 mv2 → the question asks about v, right?
To solve for v, I have to get the ω from (c). Is my idea correct?
Thanks