Find the angle of acceleration in circular motion

[trivk96]

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

 

[LawrenceC]

Don't you mean arctan rather than tan? Tan need degrees. 2.205/.98 is not degrees.

 

[trivk96]

So does that mean the answer is 66.03°

 

[LawrenceC]

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.