Question

A top of mass m = 0.50 kg, whose axis is tilted by an angle θ= 30° to the vertical, precesses due to gravity. The moment of inertia of the top relative to its symmetry axis is equal to I = 2.0 g• m², the angular velocity of rotation about that axis is equal to ω= 350 rad/s, the distance from the point of rest to the centre of inertia of the top is l= 10 cm. Find:

(a) the angular velocity of the top's precession;

(b) the magnitude and direction of the horizontal component of the reaction force acting on the top at the point of rest.

Answer 1

Here M = I ω is along the symmetry axis. It has two components, the part l ω cosθ is constant and the part M⟂ =l ω sinθ presesses, then

(b) This force is the centripetal force due to precession. It acts inward and has the magnitude

Vector ρ_i is the distance of the i th element from the axis. This is the force that the table will exert on the top.