Find the angle of acceleration in circular motion

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Homework Help Overview

The discussion revolves around determining the angle of acceleration in circular motion, specifically the relationship between tangential and centripetal acceleration. The original poster provides values for both types of acceleration and seeks to find the angle relative to the direction of motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to use the tangent function to find the angle but expresses uncertainty about the method. Some participants suggest using the arctangent function instead and clarify the relationship between the accelerations.

Discussion Status

Participants are actively discussing the correct approach to calculating the angle, with some confirming the use of arctangent and providing insights into the direction of the resultant acceleration vector. There is a focus on understanding the geometric interpretation of the vectors involved.

Contextual Notes

The original poster has not provided specific equations or methods beyond their initial attempt, and there is an ongoing exploration of the definitions and relationships between the types of acceleration in circular motion.

trivk96
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Homework Statement


Find the direction of acceleration relative to
the direction of motion. Answer between −180°
and 180°.

The tangential acceleration is .98 m/s2. The centripetal acceleration is 2.205m/s2


Answer in units of °



Homework Equations


?

The Attempt at a Solution



I tried tan( 2.205/.98) but this does not seem right at all. Could you also explain how you got the answer and why it works.


Thanks in advance
 
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Don't you mean arctan rather than tan? Tan need degrees. 2.205/.98 is not degrees.
 
So does that mean the answer is 66.03°
 
That is the arctan of 2.205/.98 so you computed the correct angle. It's 66.04 degrees measured from the tangential acceleration vector. It is pointing in the general direction of tangential acceleration but more so towards the inside of the arc because the magnitude of the centripetal acceleration is the larger of the two accelerations. If you draw the vectors to scale and place them head to tail and close the right triangle, you'll see where the resultant it is pointing.
 

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