If the velocity is v, the radius of the circle is R , then the force required is m*v

^{2}/R.

It is important to remember the force required is proportional to v

^{2}.

The force is coming from friction between object and the surface in contact.

The maximum friction force F

_{max}will determined the smallest radius of the turning circle.

i.e. R

_{min}=mv

^{2}/F

_{max}.

Your body also need to turn toward the center of the circle to keep in balance.

The best angle of the turn is determined by the horizontal friction force F

_{r}=m*v

^{2}/R and your weight (Normal force from the contact surface to the object).

The relation is tanθ= mg/Fr = g*R/v

^{2}

g is a constant (=9.8m/s

^{2}).

A larger angle is need for a smaller turn (smaller R) if the velocity is the same.

The following simulation let you play with it in 3D.

You can change the moving speed v and bending angle θ with slider.

If you click the auto check box, the object will turn the angle automatically

so the it keep turning (try it).

**Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop.**This work is licensed under a Creative Commons Attribution 2.5 Taiwan License

- Please feel free to post your ideas about how to use the simulation for better teaching and learning.
- Post questions to be asked to help students to think, to explore.
- Upload worksheets as attached files to share with more users.