Cone on horizontal surface

[phy_magic]

Homework Statement

Cone with base r and height h and period for one turn is on horizontal plane and it rotate around vertical axis.
What is expresion for friction force, it is rolling without slipping.

Relevant Equations

I observe that CM of cone rotate around vertical axis and also cone rotate around axis on which height of cone lies. There is friction force , Fg and normal force.

How to join this two rotations to find friction? If it rolls without slipping , does it mean that all contact points have same magitude of velocity like CM ( it is wierd to me because they are on diferent distance form top of cone but they all have sam angular velocitiy). Can I assume that centripetal force equals to friction force for CM?

 

[berkeman]

What does the angle of the cone need to be so that there is no frictional slipping as it rolls around that vertical axis? If the angle of the cone is not that no-slipping angle, how does friction affect each slice of the cone?

 

[haruspex]

Homework Statement: Cone with base r and height h and period for one turn is on horizontal plane and it rotate around vertical axis.

I assume the rotation rate is constant.

What is expresion for friction force, it is rolling without slipping.
Relevant Equations: I observe that CM of cone rotate around vertical axis and also cone rotate around axis on which height of cone lies. There is friction force , Fg and normal force.

What is the acceleration of the cone's mass centre? What do you deduce from that?
Would it be different if the cone were mounted on a rotating turntable instead of rolling?

If it rolls without slipping , does it mean that all contact points have same magitude of velocity like CM

If it is on a fixed surface and not slipping, what can you say about the velocities of the contact points?

 

[phy_magic]

I assume the rotation rate is constant.

What is the acceleration of the cone's mass centre? What do you deduce from that?
Would it be different if the cone were mounted on a rotating turntable instead of rolling?

If it is on a fixed surface and not slipping, what can you say about the velocities of the contact points?

What should I do about contatct point because it lies on slant of cone? Is cone motion precession of axis through vertex and normal to base?

 

[haruspex]

What should I do about contatct point because it lies on slant of cone?

Do you have to do something about the contact points? I don’t understand the question.

Is cone motion precession of axis through vertex and normal to base?

Yes.

Can you answer my questions in post #3?

 

[phy_magic]

Do you have do something about the contact points? I don’t understand the question.

Yes.

Can you answer my questions in post #3?

Cone has acceleration because of precession and I can calculate it from angular velocity and perpendicular distance between CM and verical axis .if cone is on rotating turntable iz would just rotate around axis through CM. So CM s velocity will be zero. If it rolls without slipping than contatct point will have 0 velocity with respect to lab frame(vcm=w*r) . I just don t understand what is distance r between that point and axis and through CM and is it needed fora task.

 

[haruspex]

Cone has acceleration because of precession and I can calculate it from angular velocity and perpendicular distance between CM and verical axis .

So apply $\vec F=m\vec a$ and consider what can produce that $\vec F$.

if cone is on rotating turntable iz would just rotate around axis through CM. So CM s velocity will be zero. If it rolls without slipping than contatct point will have 0 velocity with respect to lab frame(vcm=w*r) .

No, I meant with the apex of the cone at the centre of the turntable, so that the only difference from the given problem is that the cone is not rotating on its own axis.

I just don t understand what is distance r between that point and axis and through CM and is it needed fora task.

I am puzzled that you keep referring to a contact "point", as though there is only one. The cone is in contact with the plane along a line from its apex to the perimeter of its base.

 

[wrobel]

An original formulation of the problem and a picture are strongly needed.

 

[wrobel]

Cone has acceleration

A cone can not have an acceleration. A point has an acceleration.

 

[Steve4Physics]

An original formulation of the problem and a picture are strongly needed.

Possibly something like this...

A solid right circular cone of uniform density has mass m, height h and a base of radius r. ‘V’ is the cone's vertex. If required, use the fact the cone’s centre of mass is located on the cone’s internal axis, a distance 3h/4 from V.

The cone rolls, on its side, on a horizontal surface without slipping such that the cone rotates about a fixed vertical axis passing through V with a constant angular velocity [about the vertical axis] of period T.

Find the frictional force acting on the cone in terms of the given parameters.

Minor edit.

 

[Lnewqban]

If it rolls without slipping...

In what direction would the cone slip if suddenly it reaches an area of the horizontal surface having no friction?

 

[wrobel]

The formulation is still bad.

a constant angular velocity [about the vertical axis] of period T.

so we can find an acceleration of the cone’s centre of mass. Then how to use the non slippery condition?

 

[haruspex]

so we can find an acceleration of the cone’s centre of mass. Then how to use the non slippery condition?

As in post #7? Am I missing something?

 

[Steve4Physics]

The formulation is still bad.

That's a pity - I thought it [my Post #10 formulation] was quite good! How could it be improved?

so we can find an acceleration of the cone’s centre of mass.

Yes - then the solution is nearly complete (as already hinted-at by @haruspex).

Then how to use the non slippery condition?

The question does not involve a non-slippery condition. Or maybe you are referring to @Lnewqban's additional (and pedagogical) question:
EDIT: Sorry - that last bit deleted.

 

[jbriggs444]

so we can find an acceleration of the cone’s centre of mass. Then how to use the non slippery condition?

The non slippery condition would dictate the path along which the cone rolls. It would also assure us that the motion along that path is maintained by the force of static friction.

 

[Steve4Physics]

so we can find an acceleration of the cone’s centre of mass. Then how to use the non slippery condition?

The non-slipping condition is simply required to enable the cone to rotate around the vertical axis. Friction provides the centripetal force. On a frictionless surface, the centre of mass would only move in a straight line.

 

[wrobel]

The non slippery condition would dictate the path along which the cone rolls. It would also assure us that the motion along that path is maintained by the force of static friction.

yes I see