2. A fidget spinner of total spinning mass M-30g has 3 balance masses of m=4g positioned at the

radius of gyration about its centre of mass O and spin axis z of k=25mm. After the fidget spinner is

dropped it is found to shake when spunup to a speed of p=20Hz due to one of the balance masses

being pushed out by 3mm. Approximate the balance masses as point masses, assume the spinner

is thin ie 7, 7 and neglect the mass of non-spinning components.

(a) Calculate the angular momentum components and kinetic energy of the fidget spinner when

spunup to p both before and after it is dropped. Explain any differences.

(0,0,0.00236 Nms, 0.148J, 3.77x10.0.0.00236 Nms, 0.148J, unbalanced mass in xz

plane=h₂0)

(b) Determine the amplitude of the unbalanced vibratory force and moment components with respect to the body fixed axes

x,y and z both before and after it is dropped. Explain any differences.

(0,0,0 Nm, ON, 0,4.74x10.0 Nm, ON, unbalanced mass in xz plane->M₁0)

(c) Before it is dropped, the fidget spinner is made to perform a precessional motion when spunup to p by tilting it on a central

pivot (ie pencil) on Oz at a distance c-6mm. Approximate the precession rate and predict how it changes as the speed is

reduced.

(0.749 rad/s, increases)