Mini-Golf Windmill: Find Minimum Linear Speed

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SUMMARY

The discussion focuses on calculating the minimum linear speed required for a golf ball to pass through a windmill at a miniature golf course without being struck by the rotating blades. The windmill features six blades rotating at an angular speed of 1.65 rad/s, with the spacing between blades equal to their width. The golf ball, with a diameter of 0.045 m, must achieve a specific linear speed to ensure it clears the next blade safely. The relationship between angular speed and linear speed is critical for solving this problem.

PREREQUISITES
  • Understanding of angular velocity and linear velocity relationships
  • Familiarity with basic physics equations, specifically ω=θ/t and v=m/s
  • Knowledge of geometry related to circular motion
  • Ability to visualize and interpret motion in a rotating system
NEXT STEPS
  • Calculate linear speed using the formula v = rω, where r is the radius of the golf ball's path
  • Explore the concept of angular displacement in rotating systems
  • Study the effects of rotational motion on moving objects in physics
  • Investigate real-world applications of angular velocity in sports mechanics
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the dynamics of rotational motion and its practical applications in sports and engineering.

pmd28
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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.
 
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What must the ball do in the problem in order to satisfy the condition specified?
 
Go through the hole.
 
Bit more specific.
 
Go through the hole without getting hit by the windmill?
 
Oh, pfft. The golf ball has to go through the hole without getting hit by the windmill with it's slowest possible velocity.
 

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