Object Rolling: Is Acceleration of Center of Mass Possible?

In summary, friction is not given by mu * N anymore, but by (2/5) mg sin(theta). This gives the equivalent expression of friction, which is (5/7) ma.
  • #1
Kenny Lee
76
0
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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  • #2
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".
 
  • #3
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.
 
  • #4
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!
 
  • #5
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!
 
  • #6
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.)
 
  • #7
Thank you; really appreciate your help.
 

FAQ: Object Rolling: Is Acceleration of Center of Mass Possible?

Can the center of mass of an object experiencing rolling motion have acceleration?

Yes, the center of mass of an object rolling on a surface can have acceleration if there is a net force acting on the object.

How does the mass distribution of an object affect the acceleration of its center of mass during rolling?

The mass distribution of an object affects the acceleration of its center of mass during rolling as it determines the distribution of forces acting on the object. A more evenly distributed mass will result in a more uniform acceleration of the center of mass.

Is the acceleration of the center of mass of an object during rolling affected by the shape of the object?

Yes, the shape of an object can affect the acceleration of its center of mass during rolling. Objects with a larger surface area and a lower center of mass will experience more air resistance and therefore have a lower acceleration of the center of mass.

Can friction affect the acceleration of the center of mass during rolling?

Yes, friction can affect the acceleration of the center of mass during rolling. Friction between the object and the surface it is rolling on can either increase or decrease the acceleration of the center of mass, depending on the direction and magnitude of the force.

Are there any real-life applications of studying the acceleration of the center of mass during object rolling?

Yes, understanding the acceleration of the center of mass during object rolling is important in fields such as sports, engineering, and physics. For example, in sports like bowling and curling, the acceleration of the center of mass affects the trajectory and speed of the object. In engineering, the acceleration of the center of mass is important in designing vehicles and calculating the forces acting on them. In physics, it is a fundamental concept in understanding rotational motion and the conservation of energy.

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