Math Problem Statement
Solution
The problem asks us to find the linear speed for the tip of a propeller that is 3 meters long, rotating at 400 revolutions per minute. The hint suggests using as the radius.
Step-by-step Solution:
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Determine the Circumference: The propeller rotates in a circle. The formula for the circumference of a circle is: where .
Substituting:
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Calculate the Linear Speed: Linear speed can be determined using the formula: Given the number of rotations per minute is 400:
Thus, the linear speed is:
Would you like any more details or have questions?
Related Questions:
- How does changing the radius affect the linear speed?
- If the number of rotations per minute is halved, what happens to the linear speed?
- What would be the linear speed in meters per second?
- Can you calculate the angular speed of the propeller?
- How would the result change if the propeller length increased to 4 meters?
Tip: The linear speed at the tip of a rotating object is directly proportional to both its radius and the number of rotations per unit time.
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Math Problem Analysis
Mathematical Concepts
Circular Motion
Linear Speed
Revolutions per Minute (RPM)
Formulas
v = 2πr × RPM
Theorems
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Suitable Grade Level
High School (Grades 10-12)
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