Hi there!
Recall the equation for angular momentum:
[tex]L = I\omega[/tex]
L = Angular momentum (kgm²/s)
I = Moment of Inertia (kgm²)
ω = angular velocity (rad/s)
We know that the Moment of Inertia of a solid cylinder is equivalent to:
[tex]I = \frac{1}{2}MR^2[/tex]
M = mass (kg)
R = radius (m)
Plug in the givens to solve for the moment of inertia. Remember to divide the diameter by 2 for the radius, and to convert to meters.
[tex]r = \frac{d}{2} = 20/2 = 10 cm \\\\10 cm = 0.1 m[/tex]
[tex]I = \frac{1}{2}M(0.1^2) = 0.005 M[/tex]
We can rearrange the equation of angular momentum to solve for mass.
[tex]L = 0.005M * \omega\\\\\frac{L}{0.005 \omega} = M \\\\M = \frac{2}{0.005(10)} = \boxed{ 40 kg}[/tex]
