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
Explanation:
(a) The net force in the y direction is the sum of the individual forces. Taking up to be +y:
∑F = Lift − Weight
∑F = 100,000 N − 75,000 N
∑F = 25,000 N
(b) Since the net force is not 0, the forces are unbalanced.
(c) Since the lift is greater than the weight, the plane will rise.
(d) The net force in the x direction is the sum of the individual forces. Taking forward to be +x:
∑F = Thrust − Drag
∑F = 200,000 N − 23,000 N
∑F = 177,000 N
(e) Since the net force is not 0, the forces are unbalanced.
(f) Since the thrust is greater than the drag, the plane will accelerate.
Answer:
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<span>
Of course. Wind is air in motion, and the gases in air are composed of
all the usual familiar stuff ... atoms, molecules, mass, etc. That's how
the wind moves things ... it has momentum and kinetic energy, which
get transferred to the things that move in the wind.</span>
