Question

Define term of angular momentum show that the angular momentum of a particle is the product of its linear momentum and moment arm also show that angular momentum is produced only by the angular component of linear momemtum

Answer 1

Answer 4

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Answer 2

Given that,

The angular momentum of a particle is the product of its linear momentum and moment arm.

Angular momentum :

Angular momentum is equal to the product of moment of inertia and angular velocity.

In mathematically,

$L=I\times\omega$....(I)

Moment of inertia :

Moment of inertia is equal to the product of mass of object and square of radius.

In mathematically,

$I=mr^2$....(II)

Angular velocity :

Angular velocity is equal to the linear velocity divided by radius,

In mathematically,

$\omega=\dfrac{v}{r}$....(III)

We need to calculate the angular momentum of the particle

Using formula of angular momentum

$L=I\omega$

Put the value of I and $\omega$ from equation (I) and (II)

$L=mr^2\times\dfrac{v}{r}$

$L=mvr$

Hence, The angular momentum of the particle is equal to the product of the linear momentum and moment arm.