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Physics 1901 (Advanced)

Physics 1901 (Advanced). A/Prof Geraint F. Lewis Rm 557, A29 gfl@physics.usyd.edu.au www.physics.usyd.edu.au/~gfl/Lecture. Rolling without Slipping. For a rolling wheel which does not slide, then the distance it travels is related to how much it turns. Rolling without Slipping.

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Physics 1901 (Advanced)

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  1. Physics 1901 (Advanced) A/Prof Geraint F. Lewis Rm 557, A29 gfl@physics.usyd.edu.au www.physics.usyd.edu.au/~gfl/Lecture http://www.physics.usyd.edu.au/~gfl/Lecture

  2. Rolling without Slipping For a rolling wheel which does not slide, then the distance it travels is related to how much it turns. http://www.physics.usyd.edu.au/~gfl/Lecture

  3. Rolling without Slipping The total kinetic energy is and WhereC is the constant of the Moment of Inertia http://www.physics.usyd.edu.au/~gfl/Lecture

  4. Rolling without Slipping • Independent of mass & size • Any sphere beats any hoop! • What is the source of torque? Conservation of energy http://www.physics.usyd.edu.au/~gfl/Lecture

  5. Rolling without Slipping Torque is provided by friction acting at the surface (otherwise the ball would just slide). Note that the normal force does not produce a torque (although it can with deformable surfaces and rolling friction). http://www.physics.usyd.edu.au/~gfl/Lecture

  6. Rotational Work In linear mechanics, the work-kinetic energy theorem can be used to solve problems. In rotational mechanics, we note that a force, Ftan, applied to a point on a wheel always points along the direction of motion. http://www.physics.usyd.edu.au/~gfl/Lecture

  7. Rotational Work If the torque is constant Hence, we now have a rotational work-kinetic energy theorem, except http://www.physics.usyd.edu.au/~gfl/Lecture

  8. Angular Momentum In linear dynamics, complex interaction (collisions) can be examined using the conservation of momentum. In rotational dynamics, the concept of angular momentum similarly eases complex interactions. (Derivation similar to all other rotational quantities) http://www.physics.usyd.edu.au/~gfl/Lecture

  9. Angular Momentum In linear dynamics: In rotational dynamics: Hence, the net torque is equal to the rate of change of angular momentum. Hence, if there is no net torque, angular momentum is conserved. http://www.physics.usyd.edu.au/~gfl/Lecture

  10. Angular Momentum We can change the angular velocity by modifying the moment of inertia. Angular momentum is conserved, but where has the extra energy come from? http://www.physics.usyd.edu.au/~gfl/Lecture

  11. Angular Momentum I have to apply a force on the mass to change its linear velocity. Through NIII, the mass applies a force on me. For every torque there is an equal and opposite retorque. http://www.physics.usyd.edu.au/~gfl/Lecture

  12. Angular Momentum http://www.physics.usyd.edu.au/~gfl/Lecture

  13. Angular Momentum http://www.physics.usyd.edu.au/~gfl/Lecture

  14. Angular Momentum http://www.physics.usyd.edu.au/~gfl/Lecture

  15. Angular Momentum Consider a lecturer on a rotating stool holding a spinning wheel, with the axis of the wheel pointing towards the ceiling. What happens when the wheel is turned over? http://www.physics.lsa.umich.edu/demolab/demo.asp?id=696 http://www.physics.usyd.edu.au/~gfl/Lecture

  16. Angular Momentum As with linear momentum, we can use conservation of angular momentum without having to worry about the various (internal) torques in action. External torques will change the value of the total angular momentum. http://www.physics.usyd.edu.au/~gfl/Lecture

  17. Linear & Angular Momentum What is the angular momentum of an object moving along a straight line? Objects moving linearly have constant angular momentum. Rotational mechanics is linear mechanics in a different coordinate system. http://www.physics.usyd.edu.au/~gfl/Lecture

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