Question

What is the angular momentum of the disk about the axle?

Answer 1

Answer:

L =  0.5*M*R^2 * w

Explanation:

Solution:-

- The angular Momentum (L) of a rigid body about any axis is given by the following relationship:

                                     L = I*w

Where,

             I : Moment of inertia of the rigid body

             w: The angular speed of the rigid body.

- The moment of inertia (I) for a disc is given by:

                                    I = I_disc

                                    I = 0.5*M*R^2

Where,

            M : Mass of the disc

            R : The radius of the disc.

- Hence, the Angular momentum (L) of the disc rotating about an axle is:

                                  L =  0.5*M*R^2 * w

Answer 2

The angular momentum of the disk about the axle is $L = \frac{1}{2} Mr^2 \times \alpha$

The angular momentum of a disk is calculated as follows;

$L = I \alpha$

where;

• I is the moment of inertia of the disk
• α is angular acceleration

The moment of inertia of the disk is given as;

$I = \frac{1}{2} Mr^2$

Finally, we will have the following equation for angular momentum of the disk;

$L = \frac{1}{2} Mr^2 \times \alpha$

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