Can rolling without slipping occur without friction?

Physics Asked by Laboni Gautam on August 31, 2020

If a body is rolling without slipping is it necessary that there is friction acting on it ? I encountered a question in which there is a spherical body and a force is being applied on its top point …so if there is only force then it should do translation motion only .. If there is friction also then it then only it can rotate with translation am I right?

3 Answers

As outlined in my answer here this is definitely possible.

If you have an object with moment of inertia $$I=gamma mR^2$$ on a horizontal surface and you apply a constant horizontal force $$F$$ some distance $$beta R$$ above the center of the object, then for rolling without slipping to occur we need a friction force

$$f=frac{beta-gamma}{1+gamma}F$$

So whenever $$beta=gamma$$ we would have rolling without slipping with no friction. Intuitively, in this case the accelerations associated with the forces and torques balance exactly in such a way so that $$v=Romega$$ without friction needing to alter translation and/or rotation to make this true.

Some examples (some might be hard to realize in reality, but work fine mathematically):

1. The force applied to the top of a circular hoop

2. The force applied a distance $$R/2$$ above the center of a cylindrical disk

3. The force applied a distance $$2R/5$$ above the center of a solid sphere

In your case with the force being applied at the top of the sphere ($$beta=1$$), there would need to be friction though.

Answered by BioPhysicist on August 31, 2020

Rolling without slipping occurs when for the revolutionary body (RB, i.e. sphere, cylinder, disc, ring etc) the following relation holds:

$$v=Romega$$ where:

• $$v$$ is the translational velocity,
• $$omega$$ is the angular velocity,
• $$R$$ is the object's radius.

Now imagine we make a sphere rotate at $$omega$$ and we then lower it carefully on a frictionless surface, so that the translational velocity vector is parallel to the surface and perpendicular to $$vec{omega}$$ and translational velocity scalar is $$v=Romega$$.

With no forces or torques acting on the sphere because the surface is infinitely smooth, the relationship $$v=Romega$$ holds forever!

Of course one may question whether such a motion really constitutes rolling without slipping. It looks more like slipping without rolling.

But if $$v or $$v>Romega$$ then only friction can 'correct' this until $$v=Romega$$.

Answered by Gert on August 31, 2020

If there is no frictional force between an object and the surface it is moving on, then there will be no relationship (or connection) between the rate (or direction) of rotation and the translational velocity. If a horizontal force is applied to the top of a sphere on a friction-less surface, it will cause (independently) both translation and rotation. If there is friction, then the two motions will be related.

Answered by R.W. Bird on August 31, 2020

Related Questions

Force balance for belt-pulley-mass model (2nd order response system)

1  Asked on July 1, 2021 by dearn

Why “colours” of light are given in wavelength not frequency?

1  Asked on July 1, 2021

Why the transition of electron from an excited state to metastable state in a lasing medium is radiation less?

1  Asked on July 1, 2021

Can I write the scattering condition in this form?

1  Asked on July 1, 2021

Finding Mutual Capacitance of Two Identical Metal Spherical Balls?

1  Asked on July 1, 2021

How can a spinning body *suddenly* change angular momentum/KE when transitioning its axes (intersecting ellipsoids in the intermediate axis theorem)

0  Asked on July 1, 2021

Can we measure an electromagnetic field?

5  Asked on July 1, 2021 by fraschelle

Changing white light to blue light without filter?

3  Asked on July 1, 2021 by snfkin

Relation between velocity and position vector in a central force

2  Asked on July 1, 2021

Complicated partition function emerges from simple constraints

1  Asked on July 1, 2021 by jeaster

Does relativistic quantum mechanics really violate causality?

3  Asked on June 30, 2021 by sam-gralla

Young’s Double Slit Experiment: Angle between incoming waves

1  Asked on June 30, 2021

Does humidity make cold air feel colder?

5  Asked on June 30, 2021 by user27542

Different definitions of exterior derivative

2  Asked on June 30, 2021

Distinguishable, indistinguishable paramagnetic ideal gas

4  Asked on June 30, 2021 by vectorize7891

Light scattering on the rotating black hole in the Kerr geometry

1  Asked on June 30, 2021 by alex-trounev

Why do we sometimes say that we can use momentum conservation if time period is small and other we don’t?

1  Asked on June 30, 2021

Flow through constricted tube, gradual pressure increase?

0  Asked on June 30, 2021

How do the evanescent waves contribute/cause a diffraction limit?

1  Asked on June 30, 2021 by schn

Why is Power caused by the driving force?

1  Asked on June 30, 2021

Ask a Question

Get help from others!

© 2022 AnswerBun.com. All rights reserved. Sites we Love: PCI Database, MenuIva, UKBizDB, Menu Kuliner, Sharing RPP