How Do I Compute Radial Acceleration from i and j Components?

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SUMMARY

The discussion focuses on calculating the radial acceleration of a ball swinging in a vertical circle with a rope length of 1.40 m and a total acceleration vector of (−22.5i + 20.2j) m/s² at an angle of 36.1° from the lowest point. The correct method involves using the dot product of the total acceleration vector with the unit vector in the radial direction. The initial calculations provided by the user were incorrect, as they did not account for the proper vector operations needed to isolate the radial component of acceleration.

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Homework Statement


I attempted this problem, and i have a midterm tommorow. I thought my approach was correct but I don't have a clue if it actually is. I drew a simple right angle triangle according to the information given in the question.

A ball swings in a vertical circle at the end of a rope 1.40 m long. When the ball is 36.1° past the lowest point on its way up, its total acceleration is (−22.5i + 20.2j ) m/s^2. For that instant, do the following. Find the radial acceleration. Also compute the velocity at this acceleration

Homework Equations



l a l = √(ai^2 + aj^2) , ar=v^2/r

The Attempt at a Solution



l a l= √(-22.5)^2+(20.2)^2=30.24

ar=30.24cos36.1

v=√(30cos36.1)(1.4) = 5.8
 
Last edited:
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welcome to pf!

hi samatar! welcome to pf! :wink:

no, the radial component of acceleration will be the total acceleration "dot" the unit vector in the radial direction

try again :smile:​
 

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