Object Rolling: Is Acceleration of Center of Mass Possible?

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Discussion Overview

The discussion revolves around the mechanics of rolling objects, particularly focusing on the conditions under which an object rolls, the role of friction and torque, and the implications for the acceleration of the center of mass. Participants explore both theoretical and applied aspects of rolling motion, including scenarios involving inclined planes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that a torque is produced when a ball is given an initial push due to friction, leading to angular acceleration and implying accelerated motion of the center of mass.
  • Another participant clarifies that once the ball rolls without slipping, the friction force needed to maintain motion is zero on a horizontal surface, questioning the initial claim about continuous angular acceleration.
  • There is confusion about how a ball can roll without friction, with some participants referencing Newton's first law.
  • In the context of a ball rolling down an incline, participants discuss the relationship between gravitational force, friction, and acceleration, questioning whether the frictional force can be treated as a different type than the standard static friction.
  • One participant expresses uncertainty about whether the derived expressions for acceleration and friction are valid under the assumption of rolling without slipping.

Areas of Agreement / Disagreement

Participants express differing views on the role of friction in rolling motion, particularly regarding its necessity for maintaining constant speed and the nature of frictional forces on inclined planes. The discussion remains unresolved with multiple competing views on these aspects.

Contextual Notes

Some participants assume the condition of rolling without slipping without explicitly stating its implications. There is also uncertainty regarding the definitions and applicability of different types of friction in various scenarios.

Who May Find This Useful

This discussion may be of interest to students and enthusiasts of physics, particularly those exploring dynamics, mechanics of rolling motion, and the interplay between friction and acceleration.

Kenny Lee
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An object rolls because of friction yea? So does that mean a torque is produced when the ball is given an initial push? I mean there is a force, and the force is perpendicular to the line which connects to the center of rotation, so this would be logical yea?

But if there is a torque, then there is angular acceleration, since torque = I * alpha. And an angular acceleration in pure rolling implies accelerated motion of the center of mass. The ball can't be accelerating into infinity; its ridiculous. ARgh. Help me!

Any thoughts at all would be appreciated. I'm sure I went wrong somewhere.
 
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In order for the ball to start rotating, a torque is needed. Friction can provide that torque. But once the ball is able to roll without slipping, the friction force needed to maintain the motion is zero (at least on a horizontal surface). Torque is not needed to maintain a constant rotational speed.

I don't understand what you mean by "And an angular acceleration in pure rolling implies accelerated motion of the center of mass" or by "accelerating into infinity".
 
But if friction is zero, how can the ball be rolling? Or is it just N's first law in action? I don't think I'm making sense.
Yea and the latter questions are irrelevant now. Thanks.
 
Kenny Lee said:
But if friction is zero, how can the ball be rolling?
Once the ball gets rolling, friction is not needed to keep it rolling at the same speed.
Or is it just N's first law in action?
Exactly!
 
Rolling down incline

Hi.

When a ball rolls down an incline of angle theta, we say that:

mg sin(theta) - friction = ma

Then what we do is substitute the expression for friction with:

moment of inertia * angular acceleration = friction * radius of ball ---> torque

so that gives friction = (2/5) ma

And then we get:

a = (5/7) mg sin(theta).

Am I right to say that friction in this case is not given by mu * N anymore? Is this a different frictional force... although I don't see how there can be another frictional force.
OR is it an equivalent expression. In which case then, if we knew mu * N, then we can just determine acceleration from the first expression. But then, wouldn't that mean that the ball is like any other object (it could be a box, and it'd still have the same a).
OR have I got everything wrong.

Any advise would be good. Thanks!
 
Kenny Lee said:
When a ball rolls down an incline of angle theta, we say that:

mg sin(theta) - friction = ma

Then what we do is substitute the expression for friction with:

moment of inertia * angular acceleration = friction * radius of ball ---> torque

so that gives friction = (2/5) ma

And then we get:

a = (5/7) mg sin(theta).
All good. I'm sure you realize that you are implicitly assuming the "rolling without slipping" condition, which is: [itex]a = \alpha r[/itex].

Am I right to say that friction in this case is not given by mu * N anymore? Is this a different frictional force... although I don't see how there can be another frictional force.
Realize that [itex]\mu N[/itex] is the maximum available static friction force. The actual friction force will be less. (Also realize that if [itex]\theta[/itex] is too great or [itex]\mu[/itex] too low, then the static friction will not be enough to prevent slipping.)
 
Thank you; really appreciate your help.
 

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