How Do You Calculate the Total Acceleration of a Point on a Spinning Disk?

AI Thread Summary
To calculate the total acceleration of a point on a spinning disk, both tangential and centripetal accelerations must be considered. The tangential acceleration, derived from the angular acceleration, is 3 m/s², while the centripetal acceleration, calculated using the formula Ac = V² / r, is 4 m/s². Since these two accelerations are vectors acting in different directions, they cannot simply be added as scalars. Instead, the total acceleration is found by combining these vector components, typically using the Pythagorean theorem. The final magnitude of the total acceleration for the point on the disk can be determined through this vector addition approach.
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Homework Statement



A spinning disk has an angular velocity (Va) of 2 rad/s and an angular acceleration (Aa) of 3 rad/s2. A point on the disk (x) is 1 m from the center of the disk. What is the magnitude of this point x's acceleration in m/s2?

Is it the sum of the the tangential acceleration plus the centripetal acceleration?

The Attempt at a Solution



Using the angular acceleration and point x's radius I found it's acceleration to be 3 m/s^2

Then, using Ac = V2 / r, I found the centripetal acceleration to be 4 m/s2.

Now that I have these values do I add their scalar values or their vector values?
 
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The two vectors are not in the same direction. So ...?
 
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