Yes, they both cast shadows. A eclipse occurs when one enters the shadow of the other.
Solar eclipse: Earth in shadow of Moon.
Lunar eclipse: Moon in shadow of Earth.
A solar eclipse is the result of one celestial body being completely or partially obscured by another celestial body along the line of sight of an observer. A solar eclipse occurs when the moon passes between the earth and the sun, obscuring all or part of the sun's disk. A lunar eclipse occurs when the Moon passes through the Earth's shadow, making the Moon's surface completely or partially obscured.
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(a) 4.03 s
The initial angular velocity of the wheel is

The angular acceleration of the wheel is

negative since it is a deceleration.
The angular acceleration can be also written as

where
is the final angular velocity (the wheel comes to a stop)
t is the time it takes for the wheel to stop
Solving for t, we find

(b) 27.6 rad
The angular displacement of the wheel in angular accelerated motion is given by

where we have
is the initial angular velocity
is the angular acceleration
t = 4.03 s is the total time of the motion
Substituting numbers, we find

Answer:
12 kg
Explanation:
Momentum before collision = momentum after collision
m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
After the collision, they have the same velocity, so v₁ = v₂ = v:
m₁ u₁ + m₂ u₂ = m₁ v + m₂ v
m₁ u₁ + m₂ u₂ = (m₁ + m₂) v
We know that m₁ = 6 kg, u₂ = 0 m/s, and v = u₁ / 3.
(6 kg) u₁ + m₂ (0 m/s) = (6 kg + m₂) (u₁ / 3)
(6 kg) u₁ = (6 kg + m₂) (u₁ / 3)
6 kg = (6 kg + m₂) (1/3)
18 kg = 6 kg + m₂
m₂ = 12 kg