# Spinning top and Newton's Laws

Q:
Let us consider a top set to spin in outer space. The top is not to be considered a point mass. It is definitely not in "uniform motion in a straight line", so Newton's First law concerning Inertia is not applicable here. Then, some force must continuously be applied to keep it in the accelerated motion it is in. But a the force is applied only at the time of starting. So, why does it spin? Please explain .
- Ujan Chakraborty (age 15)
Kolkata,West Bengal, India
A:
You're right that every point in the top, except those exactly on the rotation axis, is accelerating, and therefore must experience a force. These forces, however, are internal ones, between different parts of the top. Newton's third law says that these forces come in pairs, so that the sum of the forces between any two parts is zero. So the total force on the top is zero. That means that its center of mass will continue in uniform non-accelerated motion. In other words, momentum is conserved.

What about the spinning motion? There's another basic principle of Newtonian physics, conservation of angular momentum.  For a collection of point particles with no other ingredients, this  principle is equivalent to saying that the force between any two points is along the line connecting them. In more complete pictures, where some momentum resides in fields, that condition doesn't hold but conservation of angular momentum still does. So no external influence is needed to keep the top spinning.

Mike W.

(published on 01/08/2013)

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