Angular momentum of a rigid body about a fixed axis is given by L=1 ωwhere I is moment of inerti

Name: Problem 59, Chapter 10: Master Resource Book in JEE Main Physics
Uploaded: 2022-03-05T13:51:01-08:00
Duration: 2 min 8 s
Channel: Bhavesh Kumar
Description: Angular momentum of a rigid body about a fixed axis is given by L=1 ωwhere I is moment of inertia and ωis angular velocity about that axis. Kinetic energy of body is given by K=(1)/(2) / ω^2 ∴ K=(1)/(2 I)(|ω)^2=(L^2)/(21) ⇒ I=(L^2)/(2 K)

step 1 Okay, the question is what is moment of inertia? Okay, in the terms of angular momentum, L and t

Question

Angular momentum of a rigid body about a fixed axis is given by $$L=1 \omega$$ where $I$ is moment of inertia and $\omega$ is angular velocity about that axis. Kinetic energy of body is given by $$ \begin{array}{ll} & K=\frac{1}{2} / \omega^{2} \\ \therefore \quad & K=\frac{1}{2 I}(\mid \omega)^{2}=\frac{L^{2}}{21} \\ \Rightarrow \quad & I=\frac{L^{2}}{2 K} \end{array} $$

   Angular momentum of a rigid body about a fixed axis is given by $$L=1 \omega$$
where $I$ is moment of inertia and $\omega$ is angular velocity about that axis.
Kinetic energy of body is given by
$$
\begin{array}{ll} 
& K=\frac{1}{2} / \omega^{2} \\
\therefore \quad & K=\frac{1}{2 I}(\mid \omega)^{2}=\frac{L^{2}}{21} \\
\Rightarrow \quad & I=\frac{L^{2}}{2 K}
\end{array}
$$

Master Resource Book in JEE Main Physics

D. B. Singh 1st Edition

Chapter 10, Problem 59

Instant Answer

Solved by Expert Bhavesh Kumar

03/05/2022

Step 1

Step 1: We know that the angular momentum of a rigid body about a fixed axis is given by $$L=I \omega$$ where $I$ is the moment of inertia and $\omega$ is the angular velocity about that axis. Show more…

Show all steps

Thanks for your feedback!

Angular momentum of a rigid body about a fixed axis is given by $$L=1 \omega$$ where $I$ is moment of inertia and $\omega$ is angular velocity about that axis. Kinetic energy of body is given by $$ \begin{array}{ll} & K=\frac{1}{2} / \omega^{2} \\ \therefore \quad & K=\frac{1}{2 I}(\mid \omega)^{2}=\frac{L^{2}}{21} \\ \Rightarrow \quad & I=\frac{L^{2}}{2 K} \end{array} $$

Play audio

Feedback

Bhavesh Kumar and 67 other subject Physics 101 Mechanics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Angular Momentum

Angular momentum is a fundamental concept in rotational dynamics that quantifies the rotational motion of a body about an axis. It is defined as the product of a body's moment of inertia and its angular velocity, and it is conserved in isolated systems where no external torques act.

Moment of Inertia

The moment of inertia is a measure of an object's resistance to angular acceleration, depending on its mass distribution relative to the axis of rotation. It plays a crucial role in determining both the angular momentum and the rotational kinetic energy of the system.

Rotational Kinetic Energy

Rotational kinetic energy is the energy an object has due to its rotation. It is calculated as one-half of the product of the moment of inertia and the square of the angular velocity, reflecting how both mass distribution and speed of rotation contribute to the energy of a rotating body.

Please give Ace some feedback