The best way to understand how tangential velocity and tangential acceleration are related is to visualize from above. Will you look at that! This video does exactly that.
Want Lecture Notes? This is an AP Physics 1 topic.
0:10 Visualizing up the three parts of the demonstration
0:51 Visualizing the tangential velocities
1:41 Visualizing the tangential accelerations
3:11 Visualizing tangential velocities and accelerations simultaneously
4:52 Angular vs. Tangential quantities
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Thank you to Christopher Becke and Natasha Trousdale for being my Quality Control Team for this video.