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A solid cylinder with diameter 20cm has an angular velocity of 10m/s and angular momentum of 2kgm^2/s. What is its mass?

Sagot :

leena

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]

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