A cylinder with rotational inertia I₁ = 2.4 kg · m² rotates clockwise about a vertical axis through its center with angular speed ω₁ = 5.8 rad/s. A second cylinder with rotational inertia I₂ = 1.3 kg · m² rotates counterclockwise about the same axis with angular speed ω₂ = 7.0 rad/s. If the cylinders couple so they have the same rotational axis, what is the angular speed of the combination (in rad/s)?

Answers :

Explanation:

Given that.

First cylinder data

Inertial I₁ = 2.4 kgm²

angular speed ω₁ = 5.8 rad/s.

Second cylinder data

inertia I₂ = 1.3 kgm²

angular speed ω₂ = 7.0 rad/s.

If the cylinders couple so they have the same rotational axis, what is the angular speed of the combination (in rad/s)?

So, the cylinder couple and move together with the same angular speed

Then, using conservation of angular momentum

L(final) = L(initial)

(I₁ + I₂) • ω = I₁•ω₁ + I₂ω₂

(2.4+1.3)•ω = 2.4 × 5.8 + 1.3 × 7

3.7•ω = 23.02

ω = 23.02 / 3.7

ω = 6.22 rad/s

The combine angular speed of the cylinder is 6.22 rad/s

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