# What is the angular momentum of an object with a mass of 5 kg that moves along a circular path of radius 3 m at a frequency of  18 Hz ?

Mar 14, 2018

$5089.38 \setminus \text{kg m"^2//"s}$

#### Explanation:

Angular momentum ($L$) is given as

L = I ω

L = mr^2 × 2 π f

Moment of inertia of small object is $m {r}^{2}$; omega = 2 π f

$L = \text{5 kg" × ("3 m")^2 × 2 × π × "18 Hz" = 5089.38\ "kg m"^2//"s}$

Mar 14, 2018

The angular momentum is $= 5089.4 k g {m}^{2} {s}^{-} 1$

#### Explanation:

The angular momentum is $L = I \omega$

where $I$ is the moment of inertia

The mass of the object is $m = 5 k g$

The radius of the path is $r = 3 m$

The moment of inertia of the object is given by

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

$= 5 \cdot {3}^{2} = 45 k g {m}^{2}$

The frequency is $f = 18 H z$

The angular velocity is $\omega = 2 \pi f = 2 \cdot 18 \cdot \pi = 36 \pi r a {\mathrm{ds}}^{-} 1$

The angular momentum is

$L = I \omega = 45 \cdot 36 \pi = 5089.4 k g {m}^{2} {s}^{-} 1$