Thursday, 4 January 2018

newtonian mechanics - Friction during pure rotation


I have already read



But I still have the following problem:





  • On one hand I've been told that if pure rotation takes place then the object goes on forever. This must imply no frictional force in any form acting on the body.




  • On the second hand I've been told that during pure rotation(no external forces like wind) on a plane surface friction acts opposite to velocity of center of mass (accompanied by change of normal) and slows it down.




Both seem logical enough:
The point of contact doesn't slip therefore no friction is required; So no retarding force and it must go on.
Things don't go on forever; Friction must be present to slow it down.


So, which hand is correct? Or is there a third hand altogether?




Answer



After researching a bit and reading the other answers, I thought it would be best if I compile everything into one answer.


Rolling friction is the opposition to rolling caused by non-ideal scenarios like wind, softness of ball, deformities, brakes(in car). Static friction is the friction which opposes the tendency of relative motion.


Instead of a ball consider a more real life car moving on a straight track.
Case 1: The engine is turned off.
Here non-ideal cases (like not a perfect roll and soft surface) slow down the car and it eventually stops. As the linear acceleration ($a$) decreases, static friction acts opposite to the motion of the car to decrease the frequency of rotation of the wheels and maintain the equation $a=\alpha r$. Static friction always tries to attain pure roll and it ends up slowing the car down.
If you consider no rolling friction then, the car is already doing pure roll and no static friction will act. And hence the car will go on forever.


Case 2: The car is accelerating.
Here the engine is increasing the frequency of the rotation of the wheels. So the point of contact has a tendency to slide instead of roll (as the linear acceleration of the car is not enough to satisfy $a=\alpha r$). So static friction acts in the direction of motion of the car so that the linear acceleration increases and the equation is maintained. So static friction here gives acceleration to the car. But Rolling friction still acts to oppose the motion as the non ideal dissipative forces already mentioned.


Case 3: The car is decelerating.

Here the frequency of rotation of the wheels is slowed down by the brakes. Static friction wants the linear acceleration to also come down to maintain pure roll. So it acts opposite to the motion of the car. Rolling friction here is still opposing the rotation of the wheel.


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