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

#### Fu-Kwun Hwang

• Hero Member
•     • • Posts: 3062 ##### Turning radius of a ski: Ski/bicycle moving in circle (circular motion in 3D)
« on: April 23, 2009, 12:12:40 pm »
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 http://www.phy.ntnu.edu.tw/ to exception site list
• 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.
Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!  #### lookang

• Hero Member
•     • • Posts: 1772
• http://weelookang.blogspot.com ##### Re: Turning radius of a ski: Ski/bicycle moving in circle (circular motion in 3D)
« Reply #1 on: June 24, 2010, 02:35:58 pm »
i am doing a project on circular motion.
this applet is fantastic for inquiry learning.
Thx!