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 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.