Answer
357.1k+ views
Hint: Angular momentum is defined as the measure of the rotational momentum of the rotating body which is equal to the product of the angular velocity of the system and the moment of the inertia to the axis. Angular momentum is a vector quantity.
Complete step by step solution:
Given data:
Initial angular momentum = L
Initial angular frequency = $\omega $
Initial Kinetic energy = k
Final angular frequency, ${\omega ‘} = 2\omega $
Final Kinetic energy, ${k’} = \dfrac{k}{2}$
Final angular momentum =?
We know that angular momentum is given by the formula, $L = mvr$
And also we know that, $v = r\omega $
Thus L can be written as, $L = m\omega {r^2}$
The kinetic energy is given by the formula, $k = \dfrac{1}{2}m{v^2}$
We can also write angular momentum in terms of Inertia and angular frequency as, $L = I\omega $
Thus kinetic energy becomes, $k = \dfrac{1}{2}I{\omega ^2}$
$\therefore $Final Inertia, ${I’} = \dfrac{1}{8}I$
Thus substituting the value of ${I’}, {\omega '}$, we get,
$\Rightarrow {L'} = \dfrac{1}{8}I \times 2\omega = \dfrac{1}{4}I\omega $ $\Rightarrow \left( {\because {L'} = {I'}{\omega '}} \right)$
$\Rightarrow {L'} = \dfrac{L}{4}$ $\left( {\because L = I\omega } \right)$
Thus the final angular momentum becomes, ${L'} = \dfrac{L}{4}$.
Hence the correct option is D.
Additional Information:
1. Kinetic energy is defined as the energy possessed by a body by its motion. It is the energy of motion.
2. Angular frequency is also called a circular frequency or radial frequency and is defined as the measurement of the angular displacement per unit time.
Note: 1. Jean Buridan who is the discoverer of momentum also discovered angular momentum.
2. As the mass increases, the angular momentum also increases. Hence we can say that the mass will be directly proportional to the angular momentum.
3. Angular momentum also depends on the rotational velocity and the rotational inertia. Whenever the object changes its shape, the angular velocity changes, and thus the angular momentum also changes.
Complete step by step solution:
Given data:
Initial angular momentum = L
Initial angular frequency = $\omega $
Initial Kinetic energy = k
Final angular frequency, ${\omega ‘} = 2\omega $
Final Kinetic energy, ${k’} = \dfrac{k}{2}$
Final angular momentum =?
We know that angular momentum is given by the formula, $L = mvr$
And also we know that, $v = r\omega $
Thus L can be written as, $L = m\omega {r^2}$
The kinetic energy is given by the formula, $k = \dfrac{1}{2}m{v^2}$
We can also write angular momentum in terms of Inertia and angular frequency as, $L = I\omega $
Thus kinetic energy becomes, $k = \dfrac{1}{2}I{\omega ^2}$
$\therefore $Final Inertia, ${I’} = \dfrac{1}{8}I$
Thus substituting the value of ${I’}, {\omega '}$, we get,
$\Rightarrow {L'} = \dfrac{1}{8}I \times 2\omega = \dfrac{1}{4}I\omega $ $\Rightarrow \left( {\because {L'} = {I'}{\omega '}} \right)$
$\Rightarrow {L'} = \dfrac{L}{4}$ $\left( {\because L = I\omega } \right)$
Thus the final angular momentum becomes, ${L'} = \dfrac{L}{4}$.
Hence the correct option is D.
Additional Information:
1. Kinetic energy is defined as the energy possessed by a body by its motion. It is the energy of motion.
2. Angular frequency is also called a circular frequency or radial frequency and is defined as the measurement of the angular displacement per unit time.
Note: 1. Jean Buridan who is the discoverer of momentum also discovered angular momentum.
2. As the mass increases, the angular momentum also increases. Hence we can say that the mass will be directly proportional to the angular momentum.
3. Angular momentum also depends on the rotational velocity and the rotational inertia. Whenever the object changes its shape, the angular velocity changes, and thus the angular momentum also changes.
Recently Updated Pages
Write a composition in approximately 450 500 words class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is the common property of the oxides CONO and class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The area of square inscribed in a circle of diameter class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Other Pages
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
In the ground state an element has 13 electrons in class 11 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Electric field due to uniformly charged sphere class 12 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
A boat takes 2 hours to go 8 km and come back to a class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
According to classical free electron theory A There class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)