Compact Disc Problem: Average Angular Acceleration

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SUMMARY

The average angular acceleration of a compact disc with inner and outer radii of 25 mm and 58 mm, respectively, can be calculated using the linear speed of 1.25 m/s. The relevant formula is v = rω, where v is the linear speed and r is the radius. The average angular acceleration can be derived from the relationship between linear and angular quantities without the need for integration, as the angular frequency ω is not constant during the disc's rotation.

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Homework Statement



The inner and outer radii of a compact disc are 25 mm and 58 mm. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.25m/s. The maximum playing time of a CD is 74.0 min. What is the average angular acceleration of a maximum-duration CD during its 74.0-min playing time? Take the direction of rotation of the disc to be positive.

Homework Equations



v=wr
angular acceleration=rw^2

The Attempt at a Solution


I tried to integrate wr somehow, but w is not constant.
 
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You don't need to integrate.

First of all, \omega, is the angular frequency. Your second formula is wrong. It should read;

a=r\omega^2 where a is the linear acceleration.

Either way, all you should need to solve this is the first formula.

You know that v=1.25m/s.

Can you use this, and your first formula to find the angular acceleration? If so, it should just be an algebra problem to find the average angular acceleration.
 

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