# Where does the centripetal force acting on a spinning top comes from?

#### Twukwuw

When a top is spinning, it wont fall down to the land as long as its angular speed is large.
I can understand this phenomena from the Torque-Angular momemtum perspective.
Howevr, i can understand it from F=ma 's perspective.

Sine its center of mass is making a circular motion around the Z-axis (not its symmetrical axis!) , there must be a centripetal force to act on it.
Where does the centripetal force comes from?

I am not sure whether i am right.....
What i also understand is :
The normal force acting on the top must be equal to the weight of the top...since the centre of mass doesnt fall
down

Can anyone explain the motion of the top's centre of mass?
Where does the centripetal force comes from??ho
Thanks!

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#### Andrew Mason

Homework Helper
Twukwuw said:
When a top is spinning, it wont fall down to the land as long as its angular speed is large.
I can understand this phenomena from the Torque-Angular momemtum perspective.
Howevr, i can understand it from F=ma 's perspective.

Sine its center of mass is making a circular motion around the Z-axis (not its symmetrical axis!) , there must be a centripetal force to act on it.
Where does the centripetal force comes from?

I am not sure whether i am right.....
What i also understand is :
The normal force acting on the top must be equal to the weight of the top...since the centre of mass doesnt fall
down

Can anyone explain the motion of the top's centre of mass?
Where does the centripetal force comes from??ho
Thanks!
The centripetal force is the supplied by the molecular forces that hold the top together.

AM

#### Twukwuw

Andrew,
The intermolecular forces between atoms or molecules can give the atoms or molecules ENOUGH centripetal force,but it never give the CENTRE of MASS centripetal force!
Just imagine there is a box, many particles there (u can imagine there is just 2 particles!) , the vector sum of the intermolecular forces will be ZERO, because every force come in pairs of SAME magnitude but DIFFERENT direction! Tjis is Newton's third law.

My question is...
When the top is spinning, and when its axis of symmetry make an angle>0 with the vertical axis, its centre of mass will make a circular motion with constant angular speed.
In other words, the top is making processional motion.
Now, What produce the centripetal force?
Is it the fiction force between the top's tip and the land?
If so, why is the direction of the fiction pointing that way?

The direction of the fiction should be in opposite direction of the centripetal force!

Thanks.

#### Andrew Mason

Homework Helper
Twukwuw said:
Andrew,
The intermolecular forces between atoms or molecules can give the atoms or molecules ENOUGH centripetal force,but it never give the CENTRE of MASS centripetal force!
Just imagine there is a box, many particles there (u can imagine there is just 2 particles!) , the vector sum of the intermolecular forces will be ZERO, because every force come in pairs of SAME magnitude but DIFFERENT direction! Tjis is Newton's third law.

My question is...
When the top is spinning, and when its axis of symmetry make an angle>0 with the vertical axis, its centre of mass will make a circular motion with constant angular speed.
In other words, the top is making processional motion.
Now, What produce the centripetal force?
Is it the fiction force between the top's tip and the land?
If so, why is the direction of the fiction pointing that way?

The direction of the fiction should be in opposite direction of the centripetal force!
If the speed of precession is slow, the friction between the base of the top and the surface it is on supplies the horizontal force to the base which, via mechanical forces that hold the top together, supplies a horizontal component of force to the top's centre of mass. If there was no horizontal friction, the center of mass would remain fixed and the axis would precess around it.

Your question about the direction of the friction force is a good one. There are two competing forces that are countered by the friction force.

1. the horizontal component of the gravitational turning force. The earth's gravity creates a torque on the centre of mass of the top (the tip of the top being the fulcrum). This is equal to the component of gravitional force perpendicular to the axis of spin multplied by the distance of the centre of mass from the tip. If the tip is to remain fixed, the surface must supply a (static friction) force equal to the horizontal component of this turning force.

2. The horizontal centripetal force on the centre of mass. Torque produces a change in angular momentum of the top. ($\tau = I\alpha$). The angular momentum must change, which means the direction of the axis must change. Since the tip is fixed, the center of mass must rotate in order for the angular momentum vector to change. As the axis directon changes, the direction of the torque changes, which causes a further and continual change in the angular momentum vector. The continual change in the direction of the axis, with the tip fixed, creates circular motion which requires a horizontal centripetal force on the centre of mass. This must be supplied by the friction at the tip, which acts in the opposite direction to the static friction force in 1.

Keep in mind that for a slowly precessing top, the centripetal force to keep the centre of mass moving in a circle is not very great.

The best illustration of this centripetal force is with a horizontally spinning gyroscope that has one end fixed to a vertical tight rope. As the gyroscope precesses, the horizontal component of the rope tension must supply the centripetal force for the gyroscope's centre of mass as it moves in a circle. You can see the rope bowing outward to supply this centripetal force.

AM

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#### drudkh

"Torque produces a change in angular momentum of the top"

The last part was a bit uncelar.
Does rotation always have a 'revolution' effect or vice versa? I mean does a rotating body tend to revolve around some central point?
If yes, then how?
If no, then how does the top start its precession?

#### Bob S

The angular momentum is a vector that precesses, but the angular momentum vector is not fixed in the top (unless it is along the largest or smallest principal moment of inertia).

There are Tippe Tops, that will stand upside down while spinning (so the tops do fall down, but the angular momentum doesn't):
http://demonstrations.wolfram.com/TippeTop/
Also see
Bob S

Last edited by a moderator:

#### Andrew Mason

Homework Helper
"Torque produces a change in angular momentum of the top"

The last part was a bit unclear
$$\tau = \dfrac{d\vec{L}}{dt}$$

If $\tau \ne 0$ then $\vec L$ (the angular momentum vector) must change with time. Since the angular momentum vector is along the axis, if there is a gravitational torque acting on the top the axis cannot stay in a fixed position. (If it did, the angular momentum vector would not change with time and this would mean there was no torque).

Does rotation always have a 'revolution' effect or vice versa? I mean does a rotating body tend to revolve around some central point?
A free rotating body revolves around its centre of mass.

If yes, then how?
If no, then how does the top start its precession?
A top starts precessing when its axis tilts ever so slightly. That results in a component of gravity perpendicular to the axis and this results in a torque on the centre of mass about the tip (provided the tip has lateral friction). That slight initial torque causes the axis to rotate, which causes the rate of change of L to increase gradually.

AM

"Where does the centripetal force acting on a spinning top comes from?"

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