Use the formula nuνequals=romegaω to find the value of the missing variable.
requals=2525 ​m, omegaωequals=StartFraction 4 pi Over 5 EndFraction
4π
5 radians per sec
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Part 1
The missing variable is nuνequals= enter your response here m per sec.
​(Type an exact​ answer.)

To solve for the missing variable \( \nu \) using the formula \( \nu = r \omega \), where:

- \( r = 25 \, \text{m} \) (radius),
- \( \omega = \frac{4\pi}{5} \, \text{radians per second} \) (angular velocity),

we simply plug in the values into the formula:

\[
\nu = 25 \times \frac{4\pi}{5}
\]

Now, calculate this step by step:

\[
\nu = 25 \times \frac{4\pi}{5} = \frac{100\pi}{5} = 20\pi
\]

So, the exact value of \( \nu \) is:

\[
\nu = 20\pi \, \text{m/s}
\]

This is the exact answer in terms of \( \pi \). If you want a decimal approximation, \( 20\pi \approx 62.83 \, \text{m/s} \).

Would you like more details or have any questions?

Here are some related questions to explore:

1. How is angular velocity \( \omega \) related to linear velocity \( \nu \)?
2. What is the physical meaning of \( \nu = r \omega \)?
3. How would the result change if the radius \( r \) were doubled?
4. What if \( \omega \) was given in degrees per second instead of radians?
5. How can this formula be applied in circular motion problems?

**Tip:** Always keep angular velocity in radians per second for easier calculation in physics-related formulas!

Use the formula \(\nu = r \omega\) to find the value of the missing variable. Given \(r = 25\, \text{m}\), \(\omega = \frac{4\pi}{5}\) radians per second. The missing variable is \(\nu = ?\) m per second. (Type an exact answer.)

Learn how to find the linear velocity using the formula \(\nu = r \omega\) in this step-by-step solution. Given a radius of 25 m and an angular velocity of \(\frac{4\pi}{5}\) radians per second, calculate the exact value of \(\nu\) in terms of \(\pi\). Perfect for high school students studying circular motion and related physics concepts.

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