Lect13-ch8ch9a_2

Lect13-ch8ch9a_2 - L13Ch8Ch9 Spring 2004 PHY 2053C: College...

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1 1 Spring 2004 PHY 2053C: College Physics A Today: finish: Rotational Motion Conservation of Angular Momentum Vector nature of quantities Static Equilibrium cancelling Torques Balance Mot i on , For c e s, Energy Heat Wave s Dr. David M. Lind Dr. Kun Yang Dr. David Van Winkle L13—Ch8Ch9 1 rot. KE 1 2 I 2 Important Points: from Last Lecture 1 Rotational Motion follows very similar laws as linear motion : Torque omes f rom for a t ng on a l ever arm : Moment of Inert a I=mr 2 s the property o a body that res sts angu ar a cc erat on: Angular Momentum is a conserved quantity, like linear momentum. Rotation carries kinetic energy I L I F r sin
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2 1 Angular Momentum As no surprise: After rotational kinetic energy comes angular momentum (analogue to linear momentum) Angular momentum has units 1 kg m 2 /s L = r p sin( ? ) “Momentum at a lever arm” Notice: different from linear momentum unit: 1 kg m/s Angular momentum is a seperately conserved quantity. You can not change angular momentum from the inside. p mv 1 Conservation of Angular Momentum It is far easier to change your moment of inertia than your mass, with or without Slim-Fast ® Bringing mass toward the axis reduces I . Conserve angular momentum : reduce I =>increase ? Examp l e o f sp i nn ng c e-skater: The rotational energy is increased, when the skater reduces her I : WHY ? HOW? I M R 2 , L I KE rot 1 2 I 2 1 2 L
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3 1 Important points 2: Linear and Angular Kinematics displacement x [m] angle ? [rad] velocity v [m/s] angular vel. ? [rad/s] ? =v / r acceleration a [m/s 2 ] angular acc. a [rad/s 2 ] Force F [N] Torque t [Nm] t =r F sin( ? ) mass m [kg] moment of inertia I [kg m 2 ] I = m r 2 momentum p [kg m/s] ang. mom. L [kg m 2 /s] p=m v L= I ?
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Lect13-ch8ch9a_2 - L13Ch8Ch9 Spring 2004 PHY 2053C: College...

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