We are asked to find the linear velocity of the tip of a windmill blade, given the following information:

• The length of the blade is 60 feet.
• The windmill rotates at a rate of 55 revolutions per minute (RPM).

Formula:

The linear velocity $V$ at the tip of a rotating object is given by: $V = \omega \times r$ where:

• $V$ is the linear velocity.
• $\omega$ is the angular velocity in radians per minute.
• $r$ is the radius of the circle (the length of the blade in this case).

Step 1: Convert RPM to angular velocity

First, convert revolutions per minute to radians per minute. Since one revolution is $2\pi$ radians, the angular velocity $\omega$ is: $\omega = 55 \, \text{revolutions/minute} \times 2\pi \, \text{radians/revolution} = 110\pi \, \text{radians/minute}$

Step 2: Multiply by the radius

Now, multiply by the radius, which is the length of the blade (60 feet): $V = 110\pi \times 60 \, \text{feet/minute}$ $V = 6600\pi \, \text{feet/minute}$ $V \approx 20734.5 \, \text{feet/minute}$

Answer:

The linear velocity of the tip of the windmill blade is approximately 20,734.5 feet per minute.

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

Here are 5 related questions for further practice:

1. What is the linear velocity if the blade length were 50 feet?
2. How many feet does the tip of the blade travel in one revolution?
3. If the windmill increased its speed to 70 RPM, what would the new linear velocity be?
4. What is the formula for angular velocity and how does it relate to RPM?
5. How would the linear velocity change if the blade were half as long?

Tip: Always ensure units are consistent when calculating velocity.