Let’s think of your cell phone as a rectangular solid of uniform density, with dimensions15 cm by 7 cm by 1 cm. imagine what would happen if you flipped it in the air (wedonotrecommend doing this with a real cell phone.)

(a) describe which axis of the phone has thegreatestmoment of inertia. call thisaxis ˆe3in the body frame of the phone.
(b) you spin the phone exactly around the axis in (a) with angular velocityω3= 20sec−1. what is the resulting motion of the phone (no torques are acting on thephone)?
(c) suppose you are not able to spin the phone exactly around the axis ˆe3, but youalso give it some angular velocityω1ω3around one of the other principal axes. show that the motion is stable, that is, thatω1andω2make small oscillations. what is the frequency of these oscillations, in sec−1? it is these little oscillationsthat make the phone wobble as it rotates through the air.