Report

Physics 7C lecture 14 Angular momentum Thursday November 14, 8:00 AM – 9:20 AM Engineering Hall 1200 Copyright © 2012 Pearson Education Inc. Torque as a vector • Torque can be expressed as a vector using the vector product. • How to find the direction of torque using a right hand rule. Copyright © 2012 Pearson Education Inc. Rigid body rotation about a moving axis • The motion of a rigid body is a combination of translational motion of the center of mass and rotation about the center of mass • The kinetic energy of a rotating and translating rigid body is K = 1/2 Mvcm2 + 1/2 Icm2. Copyright © 2012 Pearson Education Inc. Rolling without slipping • The condition for rolling without slipping is vcm = R. • Figure 10.13 shows the combined motion of points on a rolling wheel. Copyright © 2012 Pearson Education Inc. Work and power in rotational motion • The total work done on a body by the torque is equal to the change in rotational kinetic energy of the body and the power due to a torque is P = zz. Copyright © 2012 Pearson Education Inc. Angular momentum • What’s the analogue of momentum P for angular motion? Copyright © 2012 Pearson Education Inc. Angular momentum • Momentum : p = m v • angular momentum: τ = r × p = m r × v Copyright © 2012 Pearson Education Inc. Angular momentum • The angular momentum of a rigid body rotating about a symmetry axis is parallel to the angular velocity and is given by L = I. • Right hand rule! Copyright © 2012 Pearson Education Inc. Angular momentum • For any system of particles = dL/dt. • For a rigid body rotating about the z-axis z = Iz. • It makes sense! Copyright © 2012 Pearson Education Inc. Conservation of angular momentum • When the net external torque acting on a system is zero, the total angular momentum of the system is constant (conserved). Copyright © 2012 Pearson Education Inc. Conservation of angular momentum Copyright © 2012 Pearson Education Inc. Q10.11 A spinning figure skater pulls his arms in as he rotates on the ice. As he pulls his arms in, what happens to his angular momentum L and kinetic energy K? A. L and K both increase. B. L stays the same; K increases. C. L increases; K stays the same. D. L and K both stay the same. Copyright © 2012 Pearson Education Inc. A10.11 A spinning figure skater pulls his arms in as he rotates on the ice. As he pulls his arms in, what happens to his angular momentum L and kinetic energy K? A. L and K both increase. B. L stays the same; K increases. C. L increases; K stays the same. D. L and K both stay the same. Copyright © 2012 Pearson Education Inc. Conservation of angular momentum Copyright © 2012 Pearson Education Inc. A rotational “collision” • Find ω. Where is the energy lost? Copyright © 2012 Pearson Education Inc. Angular momentum in a crime bust • A bullet hits a door causing it to swing. Find ω. Copyright © 2012 Pearson Education Inc. Angular momentum in a crime bust Copyright © 2012 Pearson Education Inc. Gyroscopes and precession • For a gyroscope, the axis of rotation changes direction. The motion of this axis is called precession. Copyright © 2012 Pearson Education Inc. Non-rotating gyro Copyright © 2012 Pearson Education Inc. A rotating flywheel • For a spinning flywheel, the magnitude of the angular momentum stays the same, but its direction changes continuously. Copyright © 2012 Pearson Education Inc. A rotating flywheel • precession angular frequency: Ω = τ / L. Copyright © 2012 Pearson Education Inc. A precessing gyroscopic • What is the precession direction? CW or CCW? Copyright © 2012 Pearson Education Inc.