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

AI Thread Summary
The problem involves calculating the net acceleration of an object on a spinning disk with an angular acceleration of 12 rad/s² and a radius of 2.0 cm after 0.25 seconds. The tangential acceleration can be determined using the formula Atang = rα, resulting in a value of 24 cm/s². Additionally, the object experiences centripetal acceleration due to its circular motion, which must be calculated using the formula Ac = v²/r, where v is the tangential velocity after 0.25 seconds. The total net acceleration is the vector sum of the tangential and centripetal accelerations. Understanding these components is crucial for solving the problem accurately.
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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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