Respuesta :
Answer:
The angular velocity of the first object is twice times the angular velocity of the second object.
Explanation:
The expression for the rotational kinetic energy for first object is as follows;
[tex]K=\frac{1}{2}I \omega^{2}[/tex] ........ (1)
Here, I is the moment of inertia, K is the rotational kinetic energy and [tex] \omega^{2}[/tex] is the angular velocity.
The rotational kinetic energy for second object is as follows;
[tex]K'=\frac{1}{2}I' \omega'^{2}[/tex]
According to given condition, two objects have the same rotational kinetic energy. Object one has twice the moment of inertia than the second.
Suppose, I'=2I.
[tex]K'=\frac{1}{2}(2I) \omega'^{2}[/tex] ......... (2)
From (1) and (2),
[tex]\frac{1}{2}I \omega^{2}=\frac{1}{2}(2I) \omega'^{2}[/tex]
[tex]\omega^{2}=(2) \omega'^{2}[/tex]
[tex]\omega=2\omega'[/tex]
Therefore, the angular velocity of the first object is twice the angular velocity of the second object.
As compared to the angular velocity of the second object, the angular velocity of the first object is just half.
When an object is in rotation, its kinetic energy can be calculated by the formula given below.
[tex]K = \dfrac {1}{2} I\omega^2[/tex]
Where [tex]I[/tex] is the moment of inertia and [tex]\omega[/tex] is the angular velocity of the object.
For the given case, let us consider that,
For object 1, angular velocity is [tex]\omega_1[/tex] and moment of inertia is [tex]I_1[/tex].
For object 2, angular velocity is [tex]\omega_2[/tex] and moment of inertia is [tex]I_2[/tex].
So, the Rotational Kinetic Energy of the object 1 is,
[tex]K_1 = \dfrac {1}{2} I_1(\omega_1)^2[/tex]
The Rotational Kinetic Energy of the object 2 is
[tex]K_2 = \dfrac {1}{2} I_2(\omega_2)^2[/tex]
Object one has twice the moment of inertia than the second. Hence,
[tex]I_1 = 2 I_2[/tex]
The Rotational Kinetic Energy of the object 1 is
[tex]K_1 = \dfrac {1}{2} \times 2I_2(\omega_1)^2[/tex]
Let consider that both the objects have same rotational kinetic energy, then
[tex]K_1 = K_2[/tex]
[tex]\dfrac {1}{2} \times 2I_2(\omega_1)^2 = \dfrac {1}{2} I_2 (\omega_2)^2[/tex]
By simplifying the above equation, we get
[tex]\omega_1 = \dfrac {1}{2}\omega_2[/tex]
Hence, the angular velocity of the object 1 is half of the angular velocity of the object 2.
For more details, follow the link given below.
https://brainly.com/question/1980605.
