Relative to the positive horizontal axis, rope 1 makes an angle of 90 + 20 = 110 degrees, while rope 2 makes an angle of 90 - 30 = 60 degrees.
By Newton's second law,
where are the magnitudes of the tensions in ropes 1 and 2, respectively;
where and
.
Eliminating , we have
Solve for .
Answer:
<em>A) the moment of inertia of the system decreases and the angular speed increases. </em>
Explanation:
The complete question is
A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round. As he does this, It is true to say that
A) the moment of inertia of the system decreases and the angular speed increases.
B) the moment of inertia of the system decreases and the angular speed decreases.
C) the moment of inertia of the system decreases and the angular speed remains the same.
D) the moment of inertia of the system increases and the angular speed increases.
E) the moment of inertia of the system increases and the angular speed decreases
In angular momentum conservation, the initial angular momentum of the system is conserved, and is equal to the final angular momentum of the system. The equation of this angular momentum conservation is given as
....1
where and
are the initial and final moment of inertia respectively.
and and
are the initial and final angular speed respectively.
Also, we know that the moment of inertia of a rotating body is given as
....2
where is the mass of the rotating body,
and is the radius of the rotating body from its center.
We can see from equation 2 that decreasing the radius of rotation of the body will decrease the moment of inertia of the body.
From equation 1, we see that in order for the angular momentum to be conserved, the decrease from to
will cause the angular speed of the system to increase from
to
.
From this we can clearly see that reducing the radius of rotation will decrease the moment of inertia, and increase the angular speed.
Answer:
2.5
Explanation:
The capacitance of a parallel-plate capacitor filled with dielectric is given by
where
k is the dielectric constant
is the capacitance of the capacitor without dielectric
In this problem,
is the capacitance of the capacitor in air
is the capacitance with the dielectric inserted
Solving the equation for k, we find