The weight of an object on Earth is determined by
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Answer:
The angular velocity after the children jump off is approximately 1.4 rad/s
Explanation:
The given parameters are;
The masses of each child, m₁, and m₂ = 60 kg
The mass of the merry-go-round, m₃ = 140 kg
The initial angular velocity, = 0.75 rad/s
The angular velocity after the children jump off =
According to the principle of conservation of angular momentum
The angular momentum = I × ω
The moment of inertia, I = m × R²
The total initial angular momentum =
The total angular momentum after the children jump off =
The initial mass, = m₁ + m₂ + m₃ = 60 kg + 60 kg + 140 kg = 260 kg
The final mass, = m₃ = 140 kg
According to the principle of conservation of linear momentum, we have;
=
Therefore;
260 kg × R² × 0.75 rad/s = 140 kg × R² ×
∴ = (260 kg × R² × 0.75 rad/s)/(140 kg × R²) = 1.39285714 rad/s. ≈ 1.4 rad/s
The angular velocity after the children jump off, ≈ 1.4 rad/s.