What is the relationship between tangential and radial acceleration?

AI Thread Summary
Tangential acceleration and radial acceleration are two distinct types of acceleration that occur in circular motion, with tangential acceleration affecting the speed along the path and radial acceleration acting towards the center of the circular path. In the scenario presented, the total acceleration can be calculated using the Pythagorean theorem, as the two accelerations are perpendicular to each other. The radial acceleration is influenced by the tangential speed, which is in turn affected by the tangential acceleration. The relationship can be expressed as aTotal^2 = aTang^2 + aRad^2. Understanding this relationship is crucial for solving problems involving circular motion dynamics.
De_Dre01
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Homework Statement


qRDU6E6.png


Homework Equations


αt = r α

The Attempt at a Solution


ωi = 0 rad/s
αt = 2.00 rad/s2
r = 112 m
θ = ? at a = 6.80 m/s2

I'm not exactly sure where to begin. Help is appreciated.
 
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You have two kinds of acceleration here. Assuming the batmobile doesn't slip on the road as it's turning (radius being a constant), the two accelerations are perpendicular (one is tangential, and the other is radial (centripetal force). So you can add them like: aTotal^2 = aTang^2 + aRad^2.
One top of that, the radial acceleration is dependent on the tangential speed, so it's dependent on tangential acceleration.
 

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