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Musya8 [376]
2 years ago
9

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

Physics
1 answer:
Sati [7]2 years ago
4 0

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 = \frac{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 = \frac{d}{2} = 20/2 = 10 cm \\\\10 cm = 0.1 m

I = \frac{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\\\\\frac{L}{0.005 \omega} = M \\\\M = \frac{2}{0.005(10)} = \boxed{ 40 kg}

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