Acceleration of point of contact

Click For Summary
In a discussion about the acceleration of the point of contact for a sphere undergoing pure rolling on a smooth surface, it is established that the velocity of the point of contact is zero at any instant. The relationship between the center of mass (CM) velocity, radius, and angular speed is defined as v_cm = Rω, where ω is the angular velocity. The acceleration of the point of contact is influenced by the centripetal acceleration due to the sphere's rotation about the CM, which is Rω². While the linear acceleration of the point of contact is zero in uniform rolling, it still experiences centripetal acceleration. The clarity of the original question regarding the definition of "point of contact" is emphasized, as it can lead to different interpretations and answers.
  • #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
 

Similar threads

B Friction on pure rolling non deforming sphere?
  • · Replies 3 ·
Replies
3
Views
2K
B Two points of contact in rolling
  • · Replies 11 ·
Replies
11
Views
2K
B Rolling of non-deforming sphere on a non-deforming rough surface?
  • · Replies 4 ·
Replies
4
Views
2K
B Trouble understanding what rolling friction is
  • · Replies 9 ·
Replies
9
Views
2K
B Why is static friction necessary for pure rolling?
  • · Replies 4 ·
Replies
4
Views
3K
I A rod that falls while rotating from the end of a table
  • · Replies 2 ·
Replies
2
Views
1K
I Acceleration on an electric unicycle, how much does the rider have to lean?
  • · Replies 30 ·
2
Replies
30
Views
1K
I What is the acceleration at the contact point between a wheel and surface?
  • · Replies 17 ·
Replies
17
Views
3K
B Static friction needed for rolling without slipping
  • · Replies 4 ·
Replies
4
Views
2K
B Why Is an Object's Weight Equal to the Force of Gravity It Experiences?
  • · Replies 51 ·
2
Replies
51
Views
4K