Calculating Minimum Ball Speed for Safe Passage through Rotating Windmill Blades

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SUMMARY

The minimum speed required for a golf ball to safely pass through rotating windmill blades is determined by the angular speed of the blades and the dimensions of the ball. With the windmill rotating at 1.25 rad/s and the ball having a diameter of 0.045 m, calculations reveal that the ball must travel at a speed that allows it to clear the blade opening before the next blade arrives. Specifically, the time taken for the ball to travel 0.045 m must be less than the time it takes for the blade to rotate into position, ensuring safe passage.

PREREQUISITES
  • Understanding of angular velocity and linear speed conversion
  • Basic knowledge of kinematics, particularly distance, speed, and time relationships
  • Familiarity with rotational motion concepts
  • Ability to perform calculations involving radians and linear distances
NEXT STEPS
  • Calculate the time it takes for the windmill blade to rotate into position using the formula for angular displacement.
  • Determine the minimum linear speed of the golf ball using the relationship between distance, speed, and time.
  • Explore the effects of varying the diameter of the golf ball on the required speed for safe passage.
  • Investigate similar problems involving rotating objects and safe passage in physics contexts.
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the dynamics of rotating systems and safety calculations in motion scenarios.

mini_mia
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Hi! I'm not sure where to start on this question and I would be very thankful if somebody could help me on it:

At a mini golf course, a golf ball passes through a windmill. The windmill has 8 blades and rotates at an angular speed of 1.25 rad/s. The opening between successive blades is equal to the width of a blade. A golf ball of diameter 4.50 x 10^-2 m is just passing by one of the rotating blades. What must the minimum speed of the ball be so it won't be hit by the next blade?
 
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Hint 1: How long does it take the golf ball to travel 4.5 cm at a given speed?

Hint 2: How long is the opening available for the ball to pass through?
 
Thank you guys for trying to help me! Now I'm going to attempt to do it. :D
 

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