11317
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Disk Sliding or Rolling in a Semicircular Well
The disk of radius
in this Demonstration is acted upon by gravity,
, and either slides or rolls in the semicircular well of radius
. In reality it would only slide if the surface of the well were completely frictionless.
Contributed by:
Sarah Lichtblau
SNAPSHOTS
DETAILS
Developed from the teaching materials of Thomas Peacock and David Gossard for Course 2.003 in the Department of Mechanical Engineering at MIT.
For the most general case, the Lagrangian for the problem is given by
where
is the moment of inertia of the disk and Θ, its angle of rotation.
If the disk's motion is purely sliding,
, and the equation of motion reduces to
.
If the disk rolls without slipping, then
and the equation of motion works out to
.
RELATED LINKS
Degree of Freedom
(
ScienceWorld
)
PERMANENT CITATION
Sarah Lichtblau
"
Disk Sliding or Rolling in a Semicircular Well
"
http://demonstrations.wolfram.com/DiskSlidingOrRollingInASemicircularWell/
Wolfram Demonstrations Project
Published: January 20, 2009
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 Demonstrations
More by Author
A Rod Sliding in a Semicircular Well
Sarah Lichtblau
Motion of a Rolling Disk Driven by a Rod and Spring
Sarah Lichtblau
Motion of a Disk Hanging from a Spring on an Inclined Plane
Sarah Lichtblau
Motion of a Dumbbell Acted on by Constant Forces
Sarah Lichtblau
Falling Mass Attached to a Rigid Pulley
Sarah Lichtblau
Impulse Acting on a Pendulum
Sarah Lichtblau
Sliding or Rolling of a Sphere, Cylinder, and Tube down a Semicircular Well
Erik Mahieu
Sphere Rolling on Rails
Bernard Vuilleumier
Linear Collisions of Two Disks
Sara McCaslin and Fredericka Brown
Engineering Dynamics: Tip or Slip?
Sara McCaslin and Fredericka Brown
Related Topics
College Physics
Mechanical Engineering
Mechanics
Physics
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+