Answer :
Final answer:
The angular momentum of the stone about a line lying along the side of the roof is 60 kg·m^2/s.
Explanation:
To calculate the angular momentum of the stone about a line lying along the side of the roof, we need to consider the stone as a point mass and calculate its moment of inertia and angular velocity.
First, let's calculate the moment of inertia of the stone. Since the stone is thrown horizontally, its moment of inertia about an axis perpendicular to its motion is zero. Therefore, we only need to consider the moment of inertia about the axis lying along the side of the roof.
The moment of inertia of a point mass is given by the formula:
I = m * r^2
where m is the mass of the stone and r is the distance of the stone from the axis of rotation.
In this case, the mass of the stone is 50 g, which is equal to 0.05 kg. The distance of the stone from the axis of rotation is the height of the building, which is 30 m.
Therefore, the moment of inertia of the stone is:
I = 0.05 kg * (30 m)^2 = 45 kg·m^2
Next, let's calculate the angular velocity of the stone. The angular velocity is given by the formula:
ω = v / r
where v is the linear velocity of the stone and r is the distance of the stone from the axis of rotation.
In this case, the linear velocity of the stone is the horizontal velocity, which is 40 m/s. The distance of the stone from the axis of rotation is again the height of the building, which is 30 m.
Therefore, the angular velocity of the stone is:
ω = 40 m/s / 30 m = 4/3 rad/s
Finally, we can calculate the angular momentum of the stone using the formula:
L = I * ω
Substituting the values we calculated:
L = 45 kg·m^2 * (4/3 rad/s) = 60 kg·m^2/s
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