The problem in your screenshot asks for the angular velocity in radians per minute (rad/min) for a given revolution rate of 24 and $\frac{1}{3}$ revolutions per minute (rpm).

To find the angular velocity, we use the following formula:

$\omega = 2\pi \times \text{revolutions per minute (rpm)}$

Given that the revolutions per minute is $24 \frac{1}{3}$ rpm, which is equivalent to $24.33$ rpm, we can plug this value into the formula:

$\omega = 2\pi \times 24.33$

Calculating the angular velocity:

$\omega = 2\pi \times 24.33 \approx 152.89 \, \text{rad/min}$

This matches the value provided in your answer of $152.89 \, \text{rad/min}$.

Would you like further details on any of the steps or have additional questions?

Here are 5 related questions to further your understanding:

1. How is angular velocity related to linear velocity?
2. Why is $2\pi$ used in the formula for angular velocity?
3. What is the angular velocity if the rpm is doubled?
4. Can you express the angular velocity in radians per second instead of per minute?
5. How does changing the radius of a rotating object affect its angular velocity?

Tip: Remember that the angular velocity is always measured in radians per unit of time, while the revolutions per minute (rpm) measure the number of full rotations, so the conversion factor $2\pi$ comes from the fact that one full revolution equals $2\pi$ radians.