Chapter 10:Dynamics of Rotational MotionGoals for Chapter 10Rotational Dynamics: IPowerPoint PresentationTorqueSlide 6Slide 7Note: t = F R sinqNote: sign of tSlide 10Slide 11Work and power in rotational motionAngular momentumConservation of angular momentumSlide 15EquilibriumWalking the plankSlide 18Slide 19Hanging a farm gateCarrying a box up the stairsSlide 22How a car’s clutch workSlide 24Slide 25Slide 26A non rotating and rotating gyroscopeSlide 28Chapter 10:Dynamics of Rotational Motionr Ft = �r ruvL r P= �uv v uv0d Ldt=uv(Conservation of angular momentum)Goals for Chapter 10•Torque: “angular force”•To see how torques cause rotational dynamics (just as linear forces cause linear accelerations)•To examine the combination of translation and rotation•To calculate the work done by a torque•To study angular momentum and its conservation•To relate rotational dynamics and angular momentumRotational Dynamics: Iparticles) of group afor particle) singlefor inertia of(moment inertia of(moment )( (torque) )( 2ii22Rm I R mI R m RF R ma m F(b)(a) m1m2m3College Physics: Motion along a Straight Line The figure shows two equal-mass blocks suspended by a cord of negligible mass that runs over a pulley with half the mass of a block. The blocks are moving with constant velocity. How do the magnitudes of the forces FAand FB exerted by the cord on the two sides of the pulley compare?A. They are equal.B. FA > FB.C. FA < FB. Torque Fr Note: F(rad)has no torque with respect to ONote:  = F R sin...) distanceular (Perpendic : R or l arm Lever R F sin R F  )( RFR sin F )(Note: sign of (c.w.) mN 6.7 mN 6.7- m)N (21.7 -m)N (15.0 )1()1( )c.w.()c.c.w(2121 netmN 21.7 m)(0.866) N)(0.500 (50.06022 sin R F )(2mN 15.0 m) N)(0.300 (50.09011 sin R F )(1Work and power in rotational motionAngular momentumprL Conservation of angular momentumILmrI21L2L11I22I221iiiIK5 kgL=r x p|L|=(rp)sin90=(r)(mv)v=rConservation of LWhere did the extra 256 J come from??? oradre v 36021 Equilibriumcondition for equilibrium 00Ft==��uvvCenter of gravity is the turning pointWalking the plankA fishy wind chime0.4So that the sum of torques is equal to zeroHanging a farm gatea)What is the tension in wire CD?b)What is horizontal force on hinge B?c) What is combined vertical force on hinges A and B?Hinge A: no horizontal force!=600 NCarrying a box up the stairsTurning pointHow a car’s clutch workThe clutch disk and the gear disk is pushed into each other by two forces that do not impart any torque, what is the final angular velocity when they come together?Lz beforeLz afterIAA IBB(IA IB)finalfinalIAA IBB(IA IB)Problem 10.74Honda 600RRWho races this bike?Why can anybody race it, if he just dares to go fast?The oval track of the TexasWorld Speedway allows speedsof 250 mph.Vector nature of angular quantitiesA non rotating and rotating