Answer to Question #254588 in Physics for emy

Question

A fidget spinner of radius 0.05 m has a moment of inertia kg m2

and

is rotating at 8.4 rad s-1

. A large fly whose mass is 0.3 kg lands onto the edge of

the rotating spinner. Calculate the angular speed of the system after the fly falling

onto the spinner.

Answer 1

Given:

$r=0.05\:\rm m$

$I_0=1.25*10^{-4}\:\rm kg\cdot m^2$

$\omega_1=8.4\:\rm rad/s$

$m=0.3\:\rm kg$

The law of conservation of angular momentum

$$I_0\omega_1=(I_0+mr^2)\omega_2$$

Hence

$$\omega_2=I_0\omega_1/(I_0+mr^2)\\ =1.25*10^{-4}*8.4/(1.25*10^{-4}+0.3*0.05^2)\\ =1.2\:\rm rad/s$$