Uniform Circular Motion: Speed of the bullet

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SUMMARY

The discussion focuses on deriving a formula for the bullet speed (v) in a uniform circular motion scenario involving two disks. The key variables include the distance (D), time (T), and the angle (theta) between the holes in the disks. The relationship between speed, angular displacement, and time is established through the equations speed = 2*pi*r/T and speed = r*omega. The challenge lies in incorporating the angle theta into the speed calculation, which is essential for determining the bullet's velocity as it passes through the disks during a single revolution.

PREREQUISITES
  • Understanding of uniform circular motion principles
  • Familiarity with angular velocity (omega)
  • Knowledge of basic trigonometry and angular displacement
  • Ability to manipulate equations involving pi and circular motion
NEXT STEPS
  • Research how to calculate angular displacement in circular motion
  • Learn about the relationship between linear speed and angular speed
  • Explore the concept of velocity selectors in physics
  • Study the application of trigonometric functions in motion equations
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This discussion is beneficial for physics students, educators, and anyone interested in understanding the dynamics of uniform circular motion and its applications in velocity selection systems.

mehacute
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Homework Statement


Derive a formula for the bullet speed v in terms of D, T, and a measured angle theta between the position of the hole in the first disk and that of the hole in the second. If required, use pi, not its numeric equivalent. Both of the holes lie at the same radial distance from the shaft. theta measures the angular displacement between the two holes; for instance, \theta = 0 means that the holes are in a line and \theta=\pi means that when one hole is up, the other is down. Assume that the bullet must travel through the set of disks within a single revolution.


Homework Equations



So, I know that speed = 2*pi*r/t and that speed = r*omega. but I don't know how to factor in the theta. Can someone please derive the whole thing and explain? Thank you.


The Attempt at a Solution

 
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You didn't describe the problem completely, but I assume you're dealing with a two-disk velocity selector? The disks are moving at some angular speed omega?

If so, here's a hint: How much time does it take for a disk to move through the angle theta?
 

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