How Do You Calculate the Average Rotational Speed of a CD in Radians per Second?

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SUMMARY

The average rotational speed of a CD making 1500 revolutions in 5 minutes is calculated to be 31.4 radians per second. The calculation begins by converting the time from minutes to seconds, resulting in 300 seconds. The revolutions per second are determined to be 5 rev/s, and using the relationship that one revolution equals 2π radians, the final speed is derived using the formula ω = 2π / Δt, yielding 31.4 rad/s.

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  • Understanding of angular velocity concepts
  • Familiarity with unit conversions (minutes to seconds)
  • Knowledge of the relationship between revolutions and radians
  • Basic algebra for manipulating equations
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  • Learn about the relationship between linear and angular motion
  • Explore practical applications of rotational speed in physics
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Students in physics or engineering courses, educators teaching rotational dynamics, and anyone interested in the mathematical principles of motion.

crybllrd
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Homework Statement


If a CD makes 1500 revolutions in 5 minutes, what is the CD's average rotational speed (in units of rad/s)

Homework Equations



\omega = \frac{\Delta\theta}{\Delta t}

-or-

\omega = \frac{2\pi}{\Delta t}

The Attempt at a Solution



This problem seems a little too simple (and I didn't use the given equation), so I want to make sure I did it right:

(5min)(60s/min)=300 seconds in 5 minutes

\frac{1500rev}{300s}=5rev/s
 
Last edited:
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crybllrd said:

The Attempt at a Solution



This problem seems a little too simple (and I didn't use the given equation), so I want to make sure I did it right:

(5min)(60s/min)=300 seconds in 5 minutes

\frac{1500rev}{300s}=5rev/s

You didn't answer the question; how many radians are there in one revolution?
 
tvavanasd said:
...how many radians are there in one revolution?

\frac{300s}{1500rev}=.2s/rev

\frac{2\pi}{.2}=31.4rad
 

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