Disk spinning with object on top, find net acceleration of object

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SUMMARY

The problem involves a disk spinning with an angular acceleration of 12 rad/s² and an object placed 2.0 cm from the center. After 0.25 seconds, the net acceleration of the object can be calculated by determining both the tangential and centripetal accelerations. The tangential acceleration is found using the formula Atang = rα, resulting in 24 cm/s². The centripetal acceleration must also be calculated to find the total net acceleration of the object.

PREREQUISITES
  • Understanding of angular acceleration and its effects on linear motion
  • Familiarity with the formulas for tangential acceleration (Atang = rα) and centripetal acceleration (Ac = v²/r)
  • Basic knowledge of vector addition for combining acceleration components
  • Ability to perform calculations involving time and distance in rotational motion
NEXT STEPS
  • Calculate centripetal acceleration using the object's tangential velocity after 0.25 seconds
  • Learn about vector addition to combine tangential and centripetal accelerations
  • Explore angular motion equations to understand the relationship between angular and linear quantities
  • Study the effects of varying angular acceleration on net acceleration in rotational systems
USEFUL FOR

Students studying physics, particularly those focusing on rotational dynamics, as well as educators seeking to explain concepts of angular motion and acceleration.

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Homework Statement


A disk begins spinning from rest with angular acceleration @ = 12 rad/s^2. A small object is on the disk a distance r = 2.0 cm from the center. What is the magnitude of the net acceleration of the object after a time t = 0.25s?

(alpha) @ = 12 rad/s^2
r = 2 cm
t = 0.25 s

Homework Equations


Vtang=rw
Atang=r@
Angular motion equations..?

The Attempt at a Solution


I'm not sure where to start off with this. I actually wasn't taught this with an object placed over a spinning disk. Tangential acceleration is radius times alpha which I can use the Atang formula to get 24. From there on I'm not sure how to apply this with the time it takes to find the net acceleration of the of object.
 
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Hint: If you assume the object is stationary with respect to the disk, it has two components of acceleration. Determine them and add them as you would add any other vectors.
 

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