A hamster runs at a speed of 15 centimeters per second in a wheel of radius 8 centimeters.

a)  What is the angular velocity of the wheel? (in radians/sec)
answer can not be in decimals either a calculation or number

To find the angular velocity of the wheel, we need to use the relationship between linear velocity (speed) and angular velocity.

The formula that relates linear velocity \( v \) to angular velocity \( \omega \) is:

\[
v = \omega \times r
\]

Where:
- \( v \) is the linear velocity of the hamster, which is \( 15 \) centimeters per second.
- \( r \) is the radius of the wheel, which is \( 8 \) centimeters.
- \( \omega \) is the angular velocity, which we need to find.

Rearranging the formula to solve for \( \omega \):

\[
\omega = \frac{v}{r}
\]

Substituting the given values:

\[
\omega = \frac{15}{8} \text{ radians per second}
\]

Thus, the angular velocity of the wheel is \( \frac{15}{8} \) radians per second.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the angular velocity change if the radius of the wheel were increased?
2. If the hamster doubled its speed, what would be the new angular velocity?
3. What is the relationship between angular velocity and the time it takes for one full rotation?
4. How can angular velocity be converted to revolutions per minute (RPM)?
5. If the hamster runs for 10 seconds, how many radians does the wheel rotate?

**Tip:** When dealing with angular velocity, remember that it is often easier to work in radians, as many trigonometric functions and formulas are based on radians.

Learn how to calculate the angular velocity of a hamster wheel when given the linear speed of the hamster and the wheel's radius. This problem involves applying the relationship between linear velocity and angular velocity in rotational motion. Suitable for high school students studying physics and kinematics.

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