Introduction to physics
Introduction to physics
Lecture 21 Gyro and Statics. Motion of a gyro·Statics.Virtualwork
Lecture 21 Gyro and Statics • Motion of a gyro • Statics • Virtual work
Moving a spinning wheeliAL5Fig.20-2.AgyroscopeLo2. Taking the directions of the various quantities into account, we see thatT=XL0.(20.15)Thus,if Q and Lo are both horizontal,as shown in thefigure, is vertical.Toproduce such a torque, horizontal forces F and -F must be applied at the ends ofthe axle.How are these forces applied? By our hands, as we try to rotate the
Moving a spinning wheel
A top立F击Fig.20-3.Arapidlyspinningtop.Notethat thedirection of thetorquevectoris the direction of the precession.direction, and causes the top to precess with its axis moving in a circular cone aboutthe vertical. If is the (vertical) angular velocity of precession, we again find thatT=dL/dt=Q×LoThus, when we apply a torque to a rapidly spinning top, the direction of theprecessional motion is in the direction of the torque, or at right angles to theforces producing the torque
A top
Gyroscopic precession(a)NonrotatingflywheelfallsThe precession of agyroscope shows upF=TXWiin many commonPivot0Axis文situations.PathoffreeendCircularmotionWhentheflywheel isnotrotating,itsweight10offlywheelaxisFlywheelcreates a torquearound the pivotcausing itto fall along acircularpath until its axisrests(precession)on the table surface.Flywheelaxis(b)ViewfromaboveasflywheelfallsVPivot-dL(L=0)dLPathfolloweddLLwRotationofPivotdLbyfreeend ofdLflywheelaxisWhen theflywheel and its axis are stationaryFlywheelthey will fall to thetable surface.When theInfallingtheflywhcel rotates abouttheflywheelspins.itand itsaxis"float"intheairpivotand thus acquires an angular momentumwhile moving in a circleaboutthepivotL.The direction ofL staysconstant5
Gyroscopic precession • The precession of a gyroscope shows up in many “common” situations. 5