A wheel radius 10 inches is rotating 0.25 radians per second. What is the angular speed in degrees per second?

To convert the angular speed from radians per second to degrees per second, we use the conversion factor between radians and degrees:

\[
1 \text{ radian} = 57.2958 \text{ degrees}
\]

Given:
- Angular speed = \(0.25\) radians per second.

Now, convert this to degrees per second:

\[
\text{Angular speed in degrees per second} = 0.25 \times 57.2958 = 14.324 \text{ degrees per second}
\]

So, the angular speed is approximately **14.32 degrees per second**.

Would you like any further details or have any questions?

Here are five related questions:

1. How would you calculate the linear speed of a point on the wheel's edge?
2. What would be the angular speed in degrees per second if the wheel rotated at 1 radian per second?
3. How does the radius of the wheel affect the linear speed?
4. If the angular speed was doubled, what would the new speed be in degrees per second?
5. How would you convert an angular speed given in degrees per second to radians per second?

**Tip:** When converting between radians and degrees, always remember the key conversion: \( \pi \) radians = 180 degrees.

Understand how to convert angular speed from radians per second to degrees per second using a specific example. This problem involves converting 0.25 radians per second to degrees per second using the conversion factor between radians and degrees. Suitable for high school students studying trigonometry and angular measurements.

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