Explanation:
The sun's gravitational force is very strong. If it were not, a planet would move in a straight line out into space. The sun's gravity pulls the planet toward the sun, which changes the straight line of direction into a curve. This keeps the planet moving in an orbit around the sun
a) 6.25 rad/s
The law of conservation of angular momentum states that the angular momentum must be conserved.
The angular momentum is given by:
![L=I\omega](https://tex.z-dn.net/?f=L%3DI%5Comega)
where
I is the moment of inertia
is the angular speed
Since the angular momentum must be conserved, we can write
![L_1 = L_2\\I_1 \omega_1 = I_2 \omega_2](https://tex.z-dn.net/?f=L_1%20%3D%20L_2%5C%5CI_1%20%5Comega_1%20%3D%20I_2%20%5Comega_2)
where we have
is the initial moment of inertia
is the initial angular speed
is the final moment of inertia
is the final angular speed
Solving for
, we find
![\omega_2 = \frac{I_1 \omega_1}{I_2}=\frac{(2.25 kg m^2)(5.00 rad/s)}{1.80 kg m^2}=6.25 rad/s](https://tex.z-dn.net/?f=%5Comega_2%20%3D%20%5Cfrac%7BI_1%20%5Comega_1%7D%7BI_2%7D%3D%5Cfrac%7B%282.25%20kg%20m%5E2%29%285.00%20rad%2Fs%29%7D%7B1.80%20kg%20m%5E2%7D%3D6.25%20rad%2Fs)
b) 28.1 J and 35.2 J
The rotational kinetic energy is given by
![K=\frac{1}{2}I\omega^2](https://tex.z-dn.net/?f=K%3D%5Cfrac%7B1%7D%7B2%7DI%5Comega%5E2)
where
I is the moment of inertia
is the angular speed
Applying the formula, we have:
- Initial kinetic energy:
![K=\frac{1}{2}(2.25 kg m^2)(5.00 rad/s)^2=28.1 J](https://tex.z-dn.net/?f=K%3D%5Cfrac%7B1%7D%7B2%7D%282.25%20kg%20m%5E2%29%285.00%20rad%2Fs%29%5E2%3D28.1%20J)
- Final kinetic energy:
![K=\frac{1}{2}(1.80 kg m^2)(6.25 rad/s)^2=35.2 J](https://tex.z-dn.net/?f=K%3D%5Cfrac%7B1%7D%7B2%7D%281.80%20kg%20m%5E2%29%286.25%20rad%2Fs%29%5E2%3D35.2%20J)
Gravity and falling objects
The bending of light as it passes into a transparent material of different optical intensity is known as refraction. The correct option among all the options given in the question is option "C".It can never be
reflection as reflection is the bouncing of the light from a surface and so
option “A” can easily be negated. The last option or option
“D”<span> conversion and it mean converting something to
another and that means a total change of form. So the last option should also
be negated. The second option can also be negated.</span>
Answer:
the soap sinks because it is more dense than the duck.