Question

A uniform disk of mass 19 kg, thickness 0.5 m, and radius 0.5 m is located at the origin, oriented with its axis along the y axis. It rotates clockwise around its axis when viewed from above (that is, you stand at a point on the y axis and look toward the origin at the disk). The disk makes one complete rotation every 0.8 s. What is the rotational angular momentum of the disk

Answer 1

The rotational angular momentum is 18.653 kg m²/s

Step-by-step explanation:

The rotational angular momentum is equal to:

`L=Iw`

The moment of inertia is equal to:

`I=(1)/(2) mr^(2)`

The angular frequency is equal to:

`w=(2\pi )/(T)`

Replacing:

`L=(mr^(2)\pi )/(T) =(19*0.5^(2)*\pi )/(0.8) =18.653kgm^(2) /s`

Answer 2

Answer: 29.85 kgm²/s

Step-by-step explanation:

Given

Mass of the disk, m = 19 kg

Thickness of the disk, T = 0.5 m

Radius of the disk, r = 0.5 m

Moment of inertia of the disk, I, can be given as

I = 1/2mr², where

m = mass of the disk and

r = radius of the disk

I = 1/2 * 19 * 0.5²

I = 1/2 * 19 * 0.25

I = 1/2 * 4.75

I = 2.375 kgm²

To find the angular momentum, we know that

L = Iω where

L = angular momentum

I = moment of inertia

ω = angular velocity

Also, angular velocity, ω = 2π/T so that

ω = (2 * 3.142) / 0.5

ω = 6.284 / 0.5

ω = 12.568 rad/s

Angular momentum

L = Iω

L = 2.375 * 12.568

L = 29.849 ~ 29.85 kgm²/s

Thus, the rotational angular momentum of the disk is 29.85 kgm²/s