PhysicsPhysics 101:101: LectureLecture 1313 RotationalRotational KineticKinetic EnergyEnergy andand InertiaInertia Today’s lecture will cover Textbook Section 8.1 Prelectures/Preflights: Read the question, please. Physics 101: Lecture 13, Pg 1 LinearLinear andand AngularAngular Linear Angular Displacement x θ Velocity v ω Acceleration a α Inertia m I KE ½ m v 2 Today! N2L F = ma Momentum p = mv Physics 101: Lecture 13, Pg 2 07 EnergyEnergy ACTACT When the bucket reaches the bottom, its potential energy has decreased by an amount mgh. Where has this energy gone? A) Kinetic Energy of bucket B) Kinetic Energy of flywheel C) Both 1 and 2. Physics 101: Lecture 13, Pg 3 11 RotationalRotational Inertia,Inertia, II Tells how much “work” is required to get object spinning. Just like mass tells you how much “work” is required to get object moving. 2 Ktran = ½ m v Linear Motion ω2 Krot = ½ I Rotational Motion Σ 2 2 I = miri (units kg m ) Note! Rotational Inertia depends on what you are spinning about (basically the ri in the equation). Physics 101: Lecture 13, Pg 4 13 RotationalRotational InertiaInertia TableTable For objects with finite number of masses, use I = Σ m r 2. For “continuous” objects, use table below. Physics 101: Lecture 13, Pg 5 33 MerryMerry GoGo RoundRound Four kids (mass m) are riding on a (light) merry-go-round rotating with angular velocity ω=3 rad/s. In case A the kids are near the center (r=1.5 m), in case B they are near the edge (r=3 m). Compare the kinetic energy of the kids on the two rides. A B A) K A > K B B) K A = K B C) K A < K B Physics 101: Lecture 13, Pg 6 17 Contest!Contest! Physics 101: Lecture 13, Pg 7 InertiaInertia RodsRods Two batons have equal mass and length. Which will be “easier” to spin A) Mass on ends B) Same C) Mass in center Physics 101: Lecture 13, Pg 8 21 RollingRolling RaceRace (Hoop(Hoop vsvs Cylinder)Cylinder) A hoop and a cylinder of equal mass roll down a ramp with height h. Which has greater KE at bottom? A) Hoop B) Same C) Cylinder Physics 101: Lecture 13, Pg 9 24 PreflightPreflight RollingRolling RaceRace (Hoop(Hoop vsvs Cylinder)Cylinder) A hoop and a cylinder of equal mass roll down a ramp with height h. Which gets to the bottom of the ramp first? A) Hoop B) Same C) Cylinder Physics 101: Lecture 13, Pg 10 27 MainMain IdeasIdeas Rotating objects have kinetic energy KE = ½ I ω2 Moment of Inertia I = Σ mr 2 Depends on Mass Depends on axis of rotation Energy is conserved but need to include ω2 rotational energy too Krot = ½ I Physics 101: Lecture 13, Pg 11 30 MasslessMassless PulleyPulley ExampleExample Consider the two masses connected by a pulley as shown. Use conservation of energy to calculate the speed of the blocks after m 2 has dropped a distance h. Assume the pulley is massless. Physics 101: Lecture 13, Pg 12 37 MassiveMassive PulleyPulley ActAct Consider the two masses connected by a pulley as shown. If the pulley is massive, after m2 drops a distance h, the blocks will be moving A) faster than B) the same speed as C) slower than if it was a massless pulley Physics 101: Lecture 13, Pg 13 45 SummarySummary ω2 Rotational Kinetic Energy Krot = ½ I Σ 2 Rotational Inertia I = miri Energy Still Conserved! Physics 101: Lecture 13, Pg 14 50.