What direction does tangential velocity point?
1 answer:
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Answer:
a) I = ( +
) L² , b) w = (\frac{27 M}{18 m} + 2)⁻¹ Lv₀
Explanation:
a) The moment of inertia is a scalar that represents the inertia in circular motion, therefore it is an additive quantity.
The moment of inertia of a rod held at one end is
I₁ = 1/3 M L²
The moment of inertia of the mass at y = L
I₂ = m y²
The total inertia method
I = I₁ + I₂
I = \frac{1}{3} M L² + m (\frac{2}{3} L)²
I = ( +
) L²
b) The conservation of angular momentum, where the system is formed by the masses and the bar, in such a way that all the forces during the collision are internal.
Initial instant. Before the crash
L₀ = I₂ w₀
angular and linear velocity are related
w₀ = y v₀
w₀ = L v₀
L₀ = I₂ y v₀
Final moment. After the crash
= I w
how angular momentum is conserved
L₀ = L_{f}
I₂ y v₀ = I w
substitute
m ()² (\frac{2L}{3} v₀ = (
+
) L² w
m L³ v₀ = (
+
) L² w
m L v₀ = (
+
) w
L v₀ = w
w = (\frac{27 M}{18 m} + 2)⁻¹ Lv₀
Answer:
The original volume of the first bar is half of the original volume of the second bar.
Explanation:
The coefficient of cubic expansivity of substances is given by;
γ = ΔV ÷ (Δθ)
Given: two metal bars with equal change in volume, equal change in temperature.
Let the volume of the first metal bar be represented by , and that of the second by
.
Since they have equal change in volume,
Δ = Δ
= ΔV
For the first metal bar,
2γ = ΔV ÷ (Δθ)
⇒ Δθ = ΔV ÷ (2γ)
For the second metal bar,
γ = ΔV ÷ (Δθ)
⇒ Δθ = ΔV ÷ (γ)
Since they have equal change in temperature,
Δθ of first bar = Δθ of the second bar
ΔV ÷ (2γ) = ΔV ÷ (
γ)
So that;
(1 ÷ 2) = (1 ÷
)
2 =
=
Thus, original volume of the first bar is half of the original volume of the second bar.