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Physics 7C lecture 14. Angular momentum. Thursday November 14, 8:00 AM – 9:20 AM Engineering Hall 1200. 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. Rigid body rotation about a moving axis.

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## Angular momentum

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**Physics 7C lecture 14**• Angular momentum Thursday November 14, 8:00 AM – 9:20 AM Engineering Hall 1200**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.**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.**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.**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.**Angular momentum**• What’s the analogue of momentum P for angular motion?**Angular momentum**• Momentum : p = m v • angular momentum: τ = r × p = m r × v**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! **Angular momentum**• For any system of particles = dL/dt. • For a rigid body rotating about the z-axis z = Iz. • It makes sense!**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).**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.**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.**A rotational “collision”**• Find ω. Where is the energy lost?**Angular momentum in a crime bust**• A bullet hits a door causing it to swing. Find ω.**Gyroscopes and precession**• For a gyroscope, the axis of rotation changes direction. The motion of this axis is called precession.**A rotating flywheel**• For a spinning flywheel, the magnitude of the angular momentum stays the same, but its direction changes continuously.**A rotating flywheel**• precession angular frequency: Ω = τ / L.**A precessing gyroscopic**• What is the precession direction? CW or CCW?

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