Author Topic: Turning radius of a ski: Ski/bicycle moving in circle (circular motion in 3D)  (Read 11403 times)

Fu-Kwun Hwang

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A force which is perpendicular to the velocity is required for an object to move in circle.
If the velocity is v, the radius of the circle is R , then the force required is m*v2/R.
It is important to remember the force required is proportional to v2.
The force is coming from friction between object and the surface in contact.
The maximum friction force Fmax will determined the smallest radius of the turning circle.
i.e. Rmin=mv2/Fmax.

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 Fr=m*v2/R and your weight  (Normal force from the contact surface to the object).
 The relation is tan?= mg/Fr  = g*R/v2
g is a constant (=9.8m/s2).
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 ? with slider.
If you click the auto check box, the object will turn the angle automatically
so the it keep turning (try it).

Full screen applet or Problem viewing java?Add to exception site list
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
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i am doing a project on circular motion.
this applet is fantastic for inquiry learning.