Answer:
ω₁ / 18
Explanation:
Angular momentum is the moment of inertia times the angular velocity.
L = Iω
For a rod pivoted at its center, the moment of inertia is:
I = mr² / 12
where m is the mass and r is the length.
For the first rod:
L = (mr² / 12) ω₁
For the second rod:
L = ((2m) (3r)² / 12) ω₂
L = (18mr² / 12) ω₂
They have the same angular momentum, so:
(mr² / 12) ω₁ = (18mr² / 12) ω₂
mr² ω₁ = 18mr² ω₂
ω₁ = 18 ω₂
ω₂ = ω₁ / 18
The angular velocity of a second rod is ω₁ / 18.
Angular momentum is the moment of inertia times the angular velocity.
L = Iω
For a rod pivoted at its center, the moment of inertia is I = mr² / 12
where m is the mass and r is the length.
A rod of length r and mass m is pivoted at its center, and given an angular velocity, ω1. the second rod has the same angular momentum as the first, but whose length is 3r and whose mass is 2m.
For the first rod, angular momentum is
L = (mr² / 12) ω₁
For the second rod, angular momentum is
L = ((2m) (3r)² / 12) ω₂
L = (18mr² / 12) ω₂
They have the same angular momentum,
(mr² / 12) ω₁ = (18mr² / 12) ω₂
mr² ω₁ = 18mr² ω₂
ω₁ = 18 ω₂
ω₂ = ω₁ / 18
Thus, the angular velocity of a second rod is ω₁ / 18.
Learn more about angular momentum.
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