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?
Paradox pure rolling is a phenomenon in which an object, such as a wheel, rolls without slipping or sliding, despite the presence of friction. This is often seen in situations where the coefficient of friction is very low, and the object's angular velocity is high.
In regular rolling, there is a combination of both translational and rotational motion, where the object moves forward while also rotating. In paradox pure rolling, the object only rotates without any translational motion, even though there is friction present.
Paradox pure rolling is considered paradoxical because it goes against our common understanding of how objects move with friction. We expect that an object will experience both translational and rotational motion when there is friction, but paradox pure rolling defies this expectation.
Friction plays a crucial role in paradox pure rolling. It provides the necessary force for the object to rotate without slipping, despite the lack of translational motion. Without friction, the object would simply slide or slip instead of rolling.
One example of paradox pure rolling is seen in the motion of a rolling coin. The coin appears to roll without slipping, even though there is friction between the coin and the surface it is rolling on. Another example is seen in the motion of a spinning top on a smooth surface, where it can continue to spin without any translational motion.