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. - PowerPoint PPT PresentationTRANSCRIPT
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Angular momentum
Physics 7C lecture 14
Thursday November 14, 8:00 AM – 9:20 AMEngineering 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.
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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 Mvcm
2 + 1/2 Icm2.
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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.
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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.
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Angular momentum • What’s the analogue of momentum P for angular motion?
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Angular momentum • Momentum : p = m v
• angular momentum: τ = r × p = m r × v
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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!
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Angular momentum • For any system of particles = dL/dt.
• For a rigid body rotating about the z-axis z = Iz.
• It makes sense!
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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).
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Conservation of angular momentum
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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.
Q10.11
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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
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Conservation of angular momentum
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A rotational “collision”
• Find ω. Where is the energy lost?
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Angular momentum in a crime bust
• A bullet hits a door causing it to swing. Find ω.
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Angular momentum in a crime bust
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Gyroscopes and precession
• For a gyroscope, the axis of rotation changes direction. The motion of this axis is called precession.
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Non-rotating gyro
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A rotating flywheel• For a spinning flywheel, the magnitude of the angular
momentum stays the same, but its direction changes continuously.
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A rotating flywheel• precession angular frequency: Ω = τ / L.
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A precessing gyroscopic• What is the precession direction? CW or CCW?