Centripetal Acceleration definition help

[oneplusone]

Hello, my textbook says that the magnitude
of centripetal acceleration is equal to the sum of the forces acting on that object.
(this is in regard to an object in a circular path, by a string. See https://upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Centripetal_force_diagram.svg/220px-Centripetal_force_diagram.svg.png for an example)

I was wondering why is this so? To me, it doesn't make sense that they are equal in magnitude, since the forces are perpendicular.

Please help.

 

[rcgldr]

My textbook says that the magnitude of centripetal acceleration is equal to the sum of the forces acting on that object.

Only the sum of forces component that is perpendicular to the path of an object results in centripetal acceleration. The sum of forces component in the direction of the path of an object results in tangental acceleration.

 

[oneplusone]

So could you please briefly describe how will you solve for Tension? generically?

 

[rcgldr]

So could you please briefly describe how will you solve for Tension? generically?

The link to the diagram isn't working for me. In what direction is the string rotating, horizontally or vertically or ... ?

 

[oneplusone]

Try here.

 

[rcgldr]

Looking at that diagram, there are no other forces acting on the mass other than centripetal force, which equals m v^2 / r or m ω^2 r. The centripetal acceleration would be v^2 / r or ω^2 r.