10217

# A Massive Bar Oscillating between Two Identical Rotating Support Rollers

A heavy uniform bar of mass rests on top of two identical rollers that are continuously and rapidly turned in opposite directions with angular speed . The centers of the rollers are at a distance apart. The coefficient of kinetic friction between the bar and the roller surfaces is , a constant independent of the relative speed of the two surfaces. The bar, held at rest with its center at distance from the midpoint of the two rollers, is released at . This Demonstration depicts the subsequent motion.

### DETAILS

The motion obeys the differential equation, ; is the position of the center of gravity from the midpoint of the two rollers at an instant .
The bar executes simple harmonic motion, , for all amplitudes .
Notation:
C.G. is the center of gravity.
and are the normal forces acting on the bar through the points of the contact with the left and right cylinders, .
and are the kinetic frictional forces at the left and right contact points on the bar, and .
Reference: D. Kleppner and R. J. Kolenkow, An Introduction to Mechanics (Special Indian Edition), India: Tata McGraw–Hill, 1999 problem 6.9.

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.