Quick sign question for uniform circular motion

[hachi_roku]

Homework Statement

what is the maximum speed with which a 1500kg car can make a left turn around a curve of radius 50m on a level road without sliding?

Homework Equations

The Attempt at a Solution

i already got the answer...but my question is:

f_s points left and the equation sigmaF_r =
f_s = mv^2/r

why isn't it negative if the force in the free body is pointing left? is it because the car is turning left?

 

[Delphi51]

The F in F = mv^2/r is the force in the direction of the center of the turning circle. The friction force is in that direction, so it is positive. I don't think you want to confuse things by thinking about left and right when the essential direction is centripetal - toward the center.

 

[hachi_roku]

the book says the radial component is simply the magnitude of the vector...so in doing probs with uniform circular motion, where a is pointing towards the center...it is positive regardless of where it points in the free body diagram?

 

[Delphi51]

Yes, positive as long as it points toward the center.

 

[hachi_roku]

thank you