To find the linear speed ($v$) at the edge of a disk, we use the formula:

$v = \omega \times r$

Where:

• $v$ is the linear speed,
• $\omega$ is the angular speed,
• $r$ is the radius of the disk.

Given:

• Angular speed $\omega = 7600\pi \, \text{rad/min}$,
• Diameter of the disk = 51 mm, so the radius $r = \frac{51}{2} = 25.5 \, \text{mm}$.

Now we can plug the values into the formula:

$v = 7600\pi \times 25.5$

Let's calculate that.The linear speed at the edge of the 51 mm disk is approximately $608,841 \, \text{mm/min}$.

Would you like further details on this, or do you have any questions?

Here are 5 related questions:

1. How is angular speed related to linear speed in rotational motion?
2. What happens to linear speed if you double the disk's radius?
3. How do you convert linear speed to different units, such as meters per second?
4. What role does the angular velocity play in determining the speed at the disk's edge?
5. How would the result change if the angular speed were given in radians per second instead of per minute?

Tip: To easily switch between linear and angular motion, always remember to use the radius as the key factor!