# What is the angular momentum of an object with a mass of 4 kg that moves along a circular path of radius 2 m at a frequency of  1 Hz ?

Mar 4, 2018

Angular momentum is expressed as $I \omega$ (where, $I$ is the moment of inertia and $\omega$ is the angular velocity)

In this case given, $\nu = 1 H z$

we know, $\omega = 2 \pi \nu = 2 \pi \cdot 1 = 2 \pi r a {\mathrm{ds}}^{-} 1$

And moment of inertia of the object,w.r.t the centre of thr circular pathway it is moving is $M {r}^{2} = 4 \cdot {\left(2\right)}^{2} = 16 K g . {m}^{2}$

So,angular momentum of this object is $16 \cdot 2 \pi = 100.531 K g {m}^{2} r a {\mathrm{ds}}^{-} 1$

Mar 4, 2018

The angular momentum is $= 100.5 k g {m}^{2} {s}^{-} 1$

#### Explanation:

The angular momentum is $L = I \omega$

where $I$ is the moment of inertia

The mass of the object is $m = 4 k g$

The radius of the path is $r = 2 m$

The moment of inertia of the object is given by

$I = m {r}^{2}$

$= 4 \cdot {2}^{2} = 16 k g {m}^{2}$

The frequency is $f = 1 H z$

The angular velocity is $\omega = 2 \pi f = 2 \cdot 1 \cdot \pi = 2 \pi r a {\mathrm{ds}}^{-} 1$

The angular momentum is

$L = I \omega = 16 \cdot 2 \pi = 100.5 k g {m}^{2} {s}^{-} 1$