# Mechanics Dynamics Question

Alright so this is my question lasses and lads: a disc with a mass moment of inertia 0.125kgm^2 about its central axis is rotating at 180rad/s about the axis. What is the angular momentum of the disc about the axis?

Soo, this is what I did: $$\omega \cdot I_o= 180(\dfrac{1}{s}) \cdot 0.125(kgm^2)$$ and got $$22.5[\frac{kg m^2}{s}]$$?

But isnt that too easy? Can someone tell me if they agree or maybe if I am going wrong somewhere?

ADD: The SI unit of angular velocity is radians per second, with the radian being a dimensionless quantity, thus the SI units of angular velocity may be listed as s−1.

yes, a disk rotating about its center axis with moment of inertia I and angular velocity $$\omega$$ has angular momentum $$L$$:

$$L = I \cdot \omega$$

it is as simple as that.

• Cheers Nmech and thank you for sorting out the units. I wasn’t sure how to do that Mar 22 at 19:59

Why would you think it should be more complicated.

Angular momentum is a vector, comparable to linear momentum. And all the laws of preservation of momentum apply to it. In the most basic form if you have a particle with a mass of m moving in an arc about an axis is

• r = distance of the particle from the axis

• m= mass

• v =speed of the particle

• P = linear momentum

• $$\theta$$ = angle between the linear momentum vector, $$\vec{P}$$ and $$\vec{r}$$.

$$L = mvr sin θ = Prsin θ = \vec{P} \times \vec{r}$$

In vector notation $$L = r \times P$$.

In rigid bodies, the angular momentum is the sum of the momentum of all the particles of the body.

$$L = I \times \omega$$