Question

Can I please get this problem asap? I am unsure how to do it.

Answer 1

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:

`I_1w_1-I_2w_2=(I_1+I_2)w`

Rewrite the formula for angular velocity, w:

`w=(I_1w_1-I_2w_2)/(I_1+I_2)`

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:

`\begin{gathered} w=((1.0*20.0)-(4.0*15.0))/(1.0+4.0) \\ \\ w=(20.0-60.0)/(5.0) \\ \\ w=(-40.0)/(5.0) \\ \\ w=-8.0\text{ rad/s} \end{gathered}`

Therefore, the angular velocity for the two disk system is 8.0 rad/s clockwise.

ANSWER:

8.0 rad/s clockwise.