Given:
Moment of intertia of first disk = 1.0 kg.m²
Spinning counterclockwise at = 20.0 rad/s
Rotational intertia of second disk = 4.0 kg.m²
Spinning clockwise at 15.0 rad/s
Let's find the angular velocity of the two disk system.
To find the angular velocity, apply the formula for angular momentum conserve:
[tex]I_1w_1-I_2w_2=(I_1+I_2)w[/tex]
Rewrite the formula for angular velocity, w:
[tex]w=\frac{I_1w_1-I_2w_2}{I_1+I_2}[/tex]
Where:
I₁ = 1.0 kg.m²
w₁ = 20.0 rad/s
I₂ = 4.0 kg.m²
w₂ = 15.0 rad/s
Input values into the equation and evaluate:
[tex]\begin{gathered} w=\frac{(1.0\times20.0)-(4.0\times15.0)}{1.0+4.0} \\ \\ w=\frac{20.0-60.0}{5.0} \\ \\ w=\frac{-40.0}{5.0} \\ \\ w=-8.0\text{ rad/s} \end{gathered}[/tex]
Therefore, the angular velocity for the two disk system is 8.0 rad/s clockwise.
ANSWER:
8.0 rad/s clockwise.
