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xxphysics
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Homework Statement
The system shown in (Figure 1) consists of two balls Aand B connected by a thin rod of negligible mass. Ball Ahas three times the inertia of ball B and the distance between the two balls is ℓ. The system has a translational velocity of v in the x direction and is spinning counterclockwise at an angular speed of ω=2v/ℓ.
Homework Equations
mArA = mBrB
rA + rB = ℓ
ω = 2v/ℓ
vA = v - (2v/ℓ)rA
vB = v + (2v/ℓ)rB
3. The Attempt at a Solution
mArA = mBrB ; mA = 3mB
3mBrA = mBrB
3rA = rB
rA + rB = ℓ
rA + 3rA = ℓ
4rA = ℓ
rA/ℓ =1/4
ω = 2v/ℓ
vA = v(1 - 2rA/ℓ)
= v(1 - 2/4)
= (1/2)v
vB = v(1 + 2rB/ℓ)
= v(1 + 2(3rA)/ℓ)
= v(1 +6rA)/ℓ)
= v(1 + 6/4)
= (3/2)v
vA/vB = [(1/2)v]/[(3/2)v] = (1/2)/(3/2) = (1/2)x(2/3) = 1/3
1/3 is not the correct answer, where am I going wrong?