# 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  15 Hz ?

Dec 23, 2015

$= 1507.964 k g . {m}^{2} / s$

#### Explanation:

By definition, angular momentum is the vector cross product of the position vector from the axis of rotation to the object with the linear momentum of the object.
$\therefore \vec{L} = \vec{r} \times \vec{p}$

$= \vec{r} \times m \vec{v}$

$= r m \frac{2 \pi r}{t} \sin \theta$

$= 2 \times 4 \times \frac{2 \times \pi \times 2 \times 15}{1} \sin {90}^{\circ}$

$= 1507.964 k g . {m}^{2} / s$

(Note that frequency is the number of complete cycles or revolutions completed per second hence it makes 15 complete circles in 1 second so that how I calculated its linear speed).

Note also that the direction of the angular momentum may be found by using the right hand rule in the normal fashion, ie curl the fingers of your right hand from $\vec{r}$ to $\vec{v}$ then your thumb will point in the direction of $\vec{L}$, and will be perpendicular to both $\vec{r} \mathmr{and} \vec{v}$.