Question

A cylinder with rotational inertia I1 = 3.0 kg · m2 rotates clockwise about a vertical axis through its center with angular speed ω1 = 5.4 rad/s. A second cylinder with rotational inertia I2 = 1.3 kg · m2 rotates counterclockwise about the same axis with angular speed ω2 = 6.4 rad/s. If the cylinders couple so they have the same rotational axis, what is the angular speed of the combination (in rad/s)?

Answer 1

Answer:

ω = 1.83 rad/s clockwise

Explanation:

We are given:

I1 = 3.0kg.m2

ω1 = -5.4rad/s (clockwise being negative)

I2 = 1.3kg.m2

ω2 = 6.4rad/s  (counterclockwise being positive)

By conservation of the momentum:

I1 * ω1 + I2 * ω2 = (I1 + I2) * ω

Solving for ω:

$\omega = \frac{I1 * \omega1 + I2*\omega2}{I1+I2}=-1.83rad/s$

Since it is negative, the direction is clockwise.