Pure rolling with zero friction

Main Question or Discussion Point

when a sphere starts moving with initial velocity $v_0$ and zero angular velocity in a plane surface having friction, then first it will start rotating till it starts pure rolling. that is, its velocity of centre of mass will decrease due to backward friction and angular velocity will increase till $v_{com} = R\omega$. But after it starts pure rolling, will friction become zero?
but if friction is zero then will the ball keep tolling and never stop?
com is Centre Of Mass

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I think that the friction acting on it will be 0 from the moment it starts pure rolling. In case of pure rolling static friction acts on the object. It can change its value according to condition.

The reason it stops it that if we don't consider ideal condition then there will be slight deformation of the surface at the bottom of the sphere. And the normal force shifts to the right. So torque due to $N$ decelerates the angular velocity. So it stops after some times.

CWatters
Homework Helper
Gold Member
If an object isn't accelerating the net force acting on it must be zero.

If an object isn't accelerating the net force acting on it must be zero.
but In case of non uniform pure rolling where $a=R\alpha$ acceleration is non zero.

I think that the friction acting on it will be 0 from the moment it starts pure rolling. In case of pure rolling static friction acts on the object. It can change its value according to condition.
If you have the same sphere rolling in an inclined plane starting with $v_0$ and zero angular velocity, then initially, friction will be backward and will make the sphere start pure rolling. But then friction cant be zero after it starts pure rolling right? Because we have an $mgsin\theta$ acting at centre of mass and friction has to act in opposite direction to make the acceleration of bottom most point zero.
Also after it starts pure rolling, will the acceleration of centre of mass become zero?
What do you mean by non uniform pure rolling?

If you have the same sphere rolling in an inclined plane starting with $v_0$ and zero angular velocity, then initially, friction will be backward and will make the sphere start pure rolling. But then friction cant be zero after it starts pure rolling right? Because we have an $mgsin\theta$ acting at centre of mass and friction has to act in opposite direction to make the acceleration of bottom most point zero.
Also after it starts pure rolling, will the acceleration of centre of mass become zero?
What do you mean by non uniform pure rolling?
Initially when the CoM of the sphere is given velocity v and if it is left on a rough surface then at first kinetic friction acts on the bottom of the sphere but when $v$ becomes equal to $R\omega$ (i.e when pure rolling starts) after that static friction acts on it. And static friction can change its value according to conditions. So it will be zero because no external force acts on it other than friction acts on it. In case of incline it will not be zero because a component of $mgsin\theta$ acts as you have mentioned.

Chestermiller
Mentor
Why don't you just solve the original problem already for the case if ideal kinetic friction, using force and moment balances, and see what the answer comes out to be, rather than continuing to speculate.

Chet