Understanding Vector Addition in Acceleration Problems

AI Thread Summary
Vector addition in acceleration problems involves calculating normal and tangential acceleration, which are perpendicular to each other, resulting in a total acceleration vector at a 45-degree angle. The confusion arises when considering the angle between the total acceleration vector and the velocity vector. Speed is a scalar and does not have direction, while velocity does, meaning the angle between tangential acceleration and velocity is actually 0 degrees. Therefore, the angle between the total acceleration vector and the velocity vector cannot be 22.5 degrees as initially suggested. Visualizing the vectors helps clarify their relationships and angles.
PsychonautQQ
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Homework Statement


http://grephysics.net/ans/0177/23

The answer to this problem is confusing me.
So you can calculate the normal acceleration and tangential acceleration to each by equal and 90° apart from each other, so their final vector has an angel of 45°. However, if the speed travels in the same direction as the tangential acceleration, wouldn't the angel between the TOTAL acceleration vector and the velocity vector be 22.5° ?
 
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No, how'd you come up with 22.5 degrees? Try drawing a picture.
 
because the total acceleration vector is at a 45 degree angel, and the velocity vector would be on an axis, so wouldn't between them be 22.5?
 
PsychonautQQ said:

Homework Statement


http://grephysics.net/ans/0177/23

The answer to this problem is confusing me.
So you can calculate the normal acceleration and tangential acceleration to each by equal and 90° apart from each other, so their final vector has an angel of 45°. However, if the speed travels in the same direction as the tangential acceleration, wouldn't the angel between the TOTAL acceleration vector and the velocity vector be 22.5° ?

Speed is a scalar, it doesn't have direction. It is the velocity's magnitude and measures how quickly the particle is moving regardless of the direction of travel.
 
PsychonautQQ said:
because the total acceleration vector is at a 45 degree angel, and the velocity vector would be on an axis, so wouldn't between them be 22.5?
No, it wouldn't. Did you draw a picture? What's the angle between the tangential acceleration and the velocity?
 
vela said:
No, it wouldn't. Did you draw a picture? What's the angle between the tangential acceleration and the velocity?

0? Arn't they the same?
 

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