Rotational ConservationAngular Momentum ConservedConservationFaster RideInternal Angular MomentumInternal MovementLarger SystemGravitational TorqueGyroscopeBoomerangRotational ConservationRotational ConservationAngular Momentum Angular Momentum ConservedConservedWith no net external torque, angular momentum is With no net external torque, angular momentum is constant.constant.•The angular momentum of an isolated system is conservedThe angular momentum of an isolated system is conservedconstant0LdtLdConservationConservationWith no external torque, angular momentum is With no external torque, angular momentum is constant.constant.•dLdL//dtdt = 0= 0, , LL = constant = constantrI = mr2mr/2I = mr2/4Faster RideFaster RideA child of 180 N sits at the A child of 180 N sits at the edge of a merry-go-round edge of a merry-go-round with radius 2.0 m and mass with radius 2.0 m and mass 160 kg. The ride is spinning 160 kg. The ride is spinning with a period of 15 s.with a period of 15 s.If the child moves to the If the child moves to the center, what is the new center, what is the new period of rotation?period of rotation?The moments of inertia for The moments of inertia for the disk and combination the disk and combination were found before.were found before.•IIdd = 320 kg m = 320 kg m22•II = = IIdd + + IIcc = = 390 kg m390 kg m22The angular momentum The angular momentum comes from the period.comes from the period.•LL = = II = = II(2(2//TT))Since Since LL is conserved we can is conserved we can find the final period.find the final period.•II(2(2//TT)) = = IIdd(2(2//TTff))•TTff= = IId d TT / / II = 12 s = 12 smMrInternal Angular Internal Angular MomentumMomentumA system may have more than A system may have more than one rotating axis.one rotating axis.The total angular momentum is The total angular momentum is the sum of separate vectors.the sum of separate vectors.•LLtotaltotal = = LLss + + LLww = = LLwwLwLs = 0Internal MovementInternal MovementInternal torques cancel out.Internal torques cancel out.Conservation requires that Conservation requires that the sum stay constant.the sum stay constant.•LLtotaltotal = = LLss + (- + (-LLww) = ) = LLww•LLss = 2 = 2LLww-LwLs = 2 LwLarger SystemLarger SystemA child jumping on a merry go round adds angular A child jumping on a merry go round adds angular momentum.momentum.•Initial momentum in a straight lineInitial momentum in a straight line•Not at axis – contributes angular momentumNot at axis – contributes angular momentumLL+rpsinpGravitational TorqueGravitational TorqueTops use torque.Tops use torque.Gravity supplies the torque.Gravity supplies the torque.•The lever arm is the axis of The lever arm is the axis of rotation.rotation.•Gravity is directed down.Gravity is directed down.•The torque is at right angles to The torque is at right angles to the lever arm and horizontal.the lever arm and horizontal.The top will precess in a circle.The top will precess in a circle.mgLrGyroscopeGyroscopeA gyroscope acts like a top, and A gyroscope acts like a top, and precesses if its axis is at an precesses if its axis is at an angle.angle.If the gyroscope axis is vertical If the gyroscope axis is vertical the torque from gravity is zero.the torque from gravity is zero.If the base moves, the If the base moves, the gyroscope stays vertical.gyroscope stays vertical.mgLrBoomerangBoomerangBoomerangs move due to gravitational torque.Boomerangs move due to gravitational torque.•Aerodynamic lift is the forceAerodynamic lift is the force•The lever arm is the length of each armThe lever arm is the length of each
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