Help on Uniform Circular Motion Problem Please

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SUMMARY

The discussion focuses on deriving a formula for bullet speed (v) in relation to distance (D), time (T), and the angular displacement (θ) between two holes in rotating disks. The key equations involved are v = D/T and v = (2πr)/T, where r is the radial distance from the shaft. The challenge lies in expressing angular velocity (ω) in terms of the angle θ, which is crucial for solving the problem accurately. The participants emphasize the importance of maintaining π in the calculations to avoid errors.

PREREQUISITES
  • Understanding of uniform circular motion principles
  • Familiarity with angular velocity and its relation to linear speed
  • Basic knowledge of trigonometry, particularly angular displacement
  • Ability to manipulate equations involving π and circular geometry
NEXT STEPS
  • Research how to express angular velocity (ω) in terms of angular displacement (θ)
  • Study the relationship between linear speed and angular speed in circular motion
  • Explore the derivation of formulas involving circular motion and angular displacement
  • Practice problems involving multiple rotating disks and their interactions
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Students studying physics, particularly those focusing on mechanics and circular motion, as well as educators seeking to clarify concepts related to angular displacement and velocity.

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Homework Statement



1. Homework Statement

Derive a formula for the bullet speed v in terms of D, T, and a measured angle 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 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.

A diagram of this can be found here: http://ca.geocities.com/canbball/MRB_rr_8_a.jpg

Homework Equations



Okay so I know that v=D/t
And that v = (2\pir)/T

The Attempt at a Solution



I know that the disks rotate by 2 in time T. What I don't understand is how to express this in terms of \theta.

Any help would be greatly appreciated!
 
Last edited by a moderator:
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Can you state the angular velocity, omega, in terms of the angle theta?

In step 3, you've dropped a pi.
 

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