Mini Golf Windmill: Find Minimum Linear Speed of Ball

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To determine the minimum linear speed of a golf ball passing through a windmill with 6 blades rotating at 1.65 rad/s, one must calculate the time it takes for a blade to pass and the distance the ball needs to travel to avoid being hit. The ball's diameter is 0.045 m, which is crucial for calculating the necessary speed. The discussion highlights the importance of relating angular speed to linear distance to find the solution. Participants share insights on visualizing the problem and applying relevant equations. Ultimately, the focus is on ensuring the ball moves fast enough to clear the next blade safely.
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Homework Statement


A golf ball passing through a windmill at a miniature golf course. The windmill has 6 blades and rotates at an angular speed of 1.65 rad/s. The opening between successive blades is equal to the width of a blade. A golf ball (diameter 4.50x10-2 m) has just reached the edge of one of the rotating blades (see the drawing). Ignoring the thickness of the blades, find the minimum linear speed with which the ball moves along the ground, such that the ball will not be hit by the next blade.


Homework Equations


ω=θ/t
v=m/s


The Attempt at a Solution


I don't know how to start this. I drew out a picture and I still can't see how I can relate the equations. And the last guy helping me just stopped.
 
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hi pmd28! :smile:

the ball is 0.045 m from front to back,

so it needs to go that distance "before the gap has gone past"! :wink:
 
I knew that much, I just couldn't get θ of ω. But I slept on it and figured it out. Thanks :smile:
 

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