9716

Kinematics of a Moving Point

A point follows a path, showing its acceleration, velocity and jerk vectors attached. The path is equally defined by these vectors provided integration constants are defined. The accelerated circular motion shows why spoked wheels may have leading and trailing spokes.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

In particular, the accelerated circular motion shows that when the particle's speed is increasing, the acceleration vector rotates to lead the radius, and when the speed is decreasing, the acceleration vector rotates to trail the radius. Newton's second law states that the acceleration vector is collinear with the force vector. This is why a bicycle wheel's spoke pattern has leading spokes to efficiently transmit the pedaling torque to the wheel rim, and similarly, trailing spokes to efficiently transmit the braking torque to the rim (for wheels where the braking torque works through the hub, such as for wheels fitted with disc and coaster brakes).
For more information see Sheldon Brown's Wheel Building.
The point following an Archimedean spiral does so at a constant speed.
    • 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 »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
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+