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hms.tech
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Homework Statement
Homework Equations
F=ma
The Attempt at a Solution
I did the first three parts . The last part of this question is quite hard, i tried using Newton's 2nd law of motion but ... here is what happens :
T is the tension, as stated in the question .
so the equation of motion should be :
T cos([itex]\varphi[/itex]) = m a
Since [itex]\varphi[/itex] = pi/2 -2θ
so using some simplification we get cos[itex]\varphi[/itex]=sin(2θ)
Now, since θ is small sin(2θ) can be approximated to 2θ.
so : [itex]\frac{2Tθ}{m}[/itex] = a
for angular acceleration = α
so, α = [itex]\frac{2Tθ}{mr}[/itex]
r= a meters (the radius)
final answer (which is wrong) α = [itex]\frac{2Tθ}{ma}[/itex]
Note : a is acceleration
a is the radius given in the question
α is the angular acceleration
The correct answer given in the answer archives is :
α = -2Tθ (whoa...where did the -ve sign come from :S)
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