Calculating Linear Acceleration on a Rotating Record

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SUMMARY

The discussion focuses on calculating the linear acceleration of a point on the rim of a 30-cm-diameter record rotating at a constant angular speed of 33.5 revolutions per minute (rev/min). The correct formula for centripetal acceleration is established as \( a_c = \omega^2 r \), where \( \omega \) is the angular velocity in radians per second and \( r \) is the radius in meters. The user initially calculated an incorrect value of 3.29 m/s², while the correct centripetal acceleration is 1.8 m/s², confirming the importance of using the appropriate equations for rotational motion.

PREREQUISITES
  • Understanding of angular velocity and its conversion to radians per second
  • Familiarity with centripetal acceleration concepts
  • Basic knowledge of rotational dynamics
  • Ability to perform unit conversions and apply formulas correctly
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  • Study the derivation and application of the centripetal acceleration formula \( a_c = \omega^2 r \)
  • Learn how to convert angular speed from revolutions per minute to radians per second
  • Explore examples of linear acceleration in various rotational systems
  • Investigate the relationship between angular velocity and linear velocity in rotating objects
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Physics students, educators, and anyone interested in understanding the principles of rotational motion and centripetal acceleration in practical applications.

jenavira
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Q: What is the linear acceleration of a point on the rim of a 30-cm-diameter record rotating at a constant angular speed of 33.5 rev/min?

I seem to have all the variables and equations in hand -
r = .15m and \omega = 3.49 radians/second;
v = \omega r ;
(radial component of linear acceleration) a_r = \frac {v^2} {r} \omega^2 r

...but I get 3.29 \frac {m} {s^2} (pointing inward), and the book's answer is 1.8 \frac {m} {s^2}. Am I wrong? Is the book wrong? Did I just convert something wrong somewhere? I'm very confused.
 
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I got 1.8. You need to use the equation for centripetal acceleration (since the record is spinning) and that is ac= angular velocity^2 times radius. That should give you your answer!
 
*facepalm* Figured it was something simple like that. Thanks!
 

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