1 Answer

UDalillu · Answer 1 · 2023-09-22T01:24:48+0000

Hi there!

Recall the equation for angular momentum:

$L = I\omega$

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:

I = (1)/(2)MR^2

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.

$r = (d)/(2) = 20/2 = 10 cm \\\\10 cm = 0.1 m$

I = (1)/(2)M(0.1^2) = 0.005 M

We can rearrange the equation of angular momentum to solve for mass.

$L = 0.005M * \omega\\\\(L)/(0.005 \omega) = M \\\\M = (2)/(0.005(10)) = \boxed{ 40 kg}$

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