The discussion revolves around the concept of pure rolling motion of a rigid ball on a rigid surface, particularly focusing on the role of friction and the implications of constant velocity versus acceleration. Participants explore the conditions under which a ball can roll without slipping and the paradoxes that arise when considering friction's effects on translational and angular velocities.
Participants express differing views on the relationship between friction and pure rolling motion. There is no consensus on whether pure rolling can exist in the presence of friction, and the discussion remains unresolved regarding the implications of constant velocity versus acceleration in this context.
Participants highlight the complexity of the conditions required for rolling without slipping, including the need for specific initial velocities and the role of friction in altering motion. The discussion reflects various assumptions about the definitions and implications of rolling motion.
Why do you think there is a paradox?persia7 said:suppose a rigid ball roll on a rigid level with constant velocity , the friction on the contact surface decrease the forward velocity but increase angular velocity ,
how do you explain this paradox?
That's what I assumed.mfb said:If the ball is slipping initially, it is possible.
Doc Al said:Why do you think there is a paradox?
Not necessarily. Realize that the ball is slipping along the surface. It is not rolling without slipping.persia7 said:because increasing the angular velocity means increase forward velocity,this is paradox!
if you are right, it is impossible that there is a pure rolling in world , isn't it paradox!Doc Al said:Not necessarily. Realize that the ball is slipping along the surface. It is not rolling without slipping.
Imagine the ball is moving to the right with some initial speed V. It is not rotating. When dropped onto the surface, friction acts to the left. That friction force does two things: It creates a translational acceleration that reduces the ball's translational speed and it creates a rotational acceleration that increases the ball's angular speed.
No paradox!
What do you mean by "pure rolling"?persia7 said:if you are right, it is impossible that there is a pure rolling in world , isn't it paradox!
Doc Al said:What do you mean by "pure rolling"?
What you are calling "pure rolling" is what I usually see called "rolling without slipping". That is certainly possible.persia7 said:in pure rolling velocity of ball and surface at contact point is equal.
i said the velocity is constant . but you say the ball is accelerated , is it paradox?Doc Al said:What you are calling "pure rolling" is what I usually see called "rolling without slipping". That is certainly possible.
For an example of rolling without slipping in which friction opposes the forward velocity as it increases the angular velocity, just roll the ball down an incline. (Of course, gravity also acts.)
Sounds like you are creating impossible conditions, not a paradox. If friction is acting, how can the velocity be constant?persia7 said:i said the velocity is constant . but you say the ball is accelerated , is it paradox?
jack action said:So I would think that pure rolling without slipping cannot exist if friction is involved. Am I wrong?
It needs friction (or some other force) to accelerate, but it does not need friction to move at a constant velocity.jack action said:If a ball rolls, it needs friction, doesn't it?
No.If there is friction, then there must be a relative motion between the ball and the ground
You are.So I would think that pure rolling without slipping cannot exist if friction is involved. Am I wrong?