Question

A uniform disk has a moment of inertia that is (1/2)MR2. A uniform disk of mass 13 kg, thickness 0.3 m, and radius 0.2 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 0.3 s.
What is the rotational angular momentum of the disk?

Answer 1

Answer:

$L = 5.44 kg m^2/s$

Explanation:

here we know that

mass of the disc is m = 13 kg

here we know that radius of disc = 0.2 m

now we have moment of inertia given as

$I = \frac{1}{2}mR^2$

$I = \frac{1}{2}(13 kg)(0.2)^2$

$I = 0.26 kg m^2$

now in order to find the angular momentum we know that

$L = I\omega$

$L = 0.26 \times \omega$

here angular velocity is given by

$\omega = \frac{2\pi}{T}$

$\omega = \frac{2\pi}{0.3}$

$\omega = 21 rad/s$

now angular momentum is given as

$L = 0.26 \times 21 = 5.44 kg m^2/s$

Answer 2

The angular momentum of an object is equal to the product of its moment of inertia and angular velocity.
L = Iω
I = 1/2 MR²
I = 1/2 x 13 x (0.2)
I = 1.3

ω = 2π/t
ω = 2π/0.3
ω = 20.9

L = 1.3 x 20.9
= 27.2 kgm²/s