Acceleration of point of contact

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SUMMARY

The discussion centers on the acceleration of the point of contact of a sphere undergoing pure rolling on a smooth surface, with a constant center of mass velocity. It is established that the velocity of the point of contact is zero during rolling motion, leading to the conclusion that the linear acceleration of the point of contact is also zero in uniform rolling. However, the point of contact experiences centripetal acceleration due to its rotation about the center of mass, which is expressed as Rω², where R is the radius and ω is the angular velocity of the sphere.

PREREQUISITES
  • Understanding of pure rolling motion
  • Knowledge of angular velocity and angular acceleration
  • Familiarity with centripetal acceleration concepts
  • Basic principles of kinematics in rotational motion
NEXT STEPS
  • Study the relationship between linear and angular motion in rolling objects
  • Explore the derivation of acceleration formulas for rolling spheres
  • Investigate the effects of friction on rolling motion
  • Learn about cycloidal motion and its implications in rolling dynamics
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the dynamics of rolling motion and rotational kinematics.

  • #31
quawa99 said:
For a sphere undergoing pure rolling on a smooth surface with center of mass having constant velocity,what is the acceleration of point of contact

You've got different answers because your question isn't clear. What do you mean by "point of contact"? Three possible interpretations and related answers:

1) a virtual point that moves along the surface so as to coincide always with the surface's point that touches the sphere. Its speed is constant, so it's acceleration is zero.

2) the material point of the flat surface that, at a given instant, touches the sphere. It does not move: speed zero, acceleration zero.

3) the material point of the sphere's surface that, at a given instant, touches the flat surface. This is the most interesting case. Its trajectory is an ordinary cycloid, its instantaneous speed is zero, however, its acceleration is the centripetal acceleration it had if the sphere were only rotating (no translation) around the same axis with same angular speed. Can you see why?

--
TRu-TS
Buon vento e cieli sereni
 

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