Tangential and radial acceleration

[MechaMZ]

Homework Statement

A ball swings in a vertical circle at the end of a rope 1.50 m long. When the ball is 37.5° past the lowest point on its way up, its total acceleration is (-22.5 i + 20.2 j) m/s².

The Attempt at a Solution

Determine the magnitude of its radial acceleration.

My attempt, but wrong answer.
1. total acceleration = 30.237, by resolving (-22.5 i + 20.2 j) m/s² into R
2. build a geometry triangle, to calculate a_r
30.237sin 37.5 = a_r

Homework Statement

I think the ans should about 27-29m/s²

Homework Equations

The Attempt at a Solution

 

[Doc Al]

You found the magnitude of the total acceleration, but what about its direction?

Hint: Try working with each component of the total acceleration. How much of each component is in the radial direction?

 

[MechaMZ]

I think I understand now, there shouldn't have any tangential acceleration for this uniform circular motion. so the R is the a_c.

Thank you Doc Al


more information about this question: https://www.physicsforums.com/showthread.php?t=308138

 

[Doc Al]

I think I understand now, there shouldn't have any tangential acceleration for this uniform circular motion. so the R is the a_c.

This isn't uniform circular motion and the acceleration will have a tangential component. But no need to guess. Figure out the direction of the acceleration and how it compares with the direction of the rope.