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PH 201

PH 201. Dr. Cecilia Vogel Lecture 20. REVIEW. Constant angular acceleration equations Rotational Motion torque. OUTLINE. moment of inertia angular momentum angular kinetic energy. Table so Far. Recall Momentum. Momentum is conserved, if no external force because S F=m D v CM / D t

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PH 201

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  1. PH 201 Dr. Cecilia Vogel Lecture 20

  2. REVIEW • Constant angular acceleration equations • Rotational Motion • torque OUTLINE • moment of inertia • angular momentum • angular kinetic energy

  3. Table so Far

  4. Recall Momentum • Momentum is conserved, • if no external force • because • SF=mDvCM/Dt • So if LHS=0, DvCM=0 • then Dp=0

  5. Angular Momentum • St=IDw/Dt • So if LHS =0 • then IDw = 0 • Define angular momentum • Angular momentum conserved • if no net external torque

  6. Linear variable Angular variable Variable name x q angle (rad) v = dx/dt w = dq/dt angular velocity (rad/s) a = dv/dt a = dw/dt ang. acceleration (rad/s2) F t torque (Nm) m I moment of inertia (kgm2) K = ½mv2 Krot = ½Iw2 Rotational Kinetic Energy (J) p Add to Table Angular momentum (kgm2/s) L=Iw

  7. Angular Momentum • St=IDw/Dt • So if net torque is not zero • then L changes • angular momentum changes

  8. Angular Momentum • angular momentum is a vector • direction is found by a RHR • Hold your right hand so your curved fingers point in the direction of rotation • then your thumb will point in the direction of angular momentum (out +, in -)

  9. Conservation Demo • Sit on a chair, free to rotate • hold a wheel rotating so its angular momentum points to your left. • Try to tip wheel’s axis up or down. • Notice • torque required for you to change angular momentum of wheel (just direction). • You and wheel are isolated, so if you tip wheel axis down, • to conserve momentum need L ___.

  10. Demo and Bikes • Sit on a bike • wheels rotate so angular momentum points to your left. • Lean the bike. • If you tip wheel axis down, (lean left) • to conserve momentum need L ___ • Bike turns ___

  11. Kinetic Energy of Rotation • As a rigid body rotates, • all parts are moving • but different parts are moving at different speeds, • so • If you consider • then

  12. Add to Table

  13. Total Kinetic Energy • An object might be rotating, while also moving linearly, • like a tire on a bike that’s being ridden. • Has • and note: Krot must be rotation about CM

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