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Final exam: room 105 HECC, 8-10 am, Wednesday, December 12 th

Final exam: room 105 HECC, 8-10 am, Wednesday, December 12 th. Kinematics. If. is given, you can find. and. Kinematics of circular motion. If. is given, you can find. and. by integration,. similarly to linear motion. General motion. y. x. Dynamics I. Newton’s First Law

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Final exam: room 105 HECC, 8-10 am, Wednesday, December 12 th

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  1. Final exam: room 105 HECC, 8-10 am, Wednesday, December 12th

  2. Kinematics If is given, you can find and

  3. Kinematics of circular motion If is given, you can find and by integration, similarly to linear motion

  4. General motion y x

  5. Dynamics I Newton’s First Law Second Law Third Law

  6. A Recipe for Solving Problems • Sketch • Isolate the body (only external forces but not forces that one part of the object exert on another part); • Identify all forces, maybe using 3rd law • 2. Write down 2nd Newton’s law Choose a coordinate system Write 2nd Newton’s law in component form: You can use different coordinates for different bodies, but be careful to relate them properly. 3. Solve for acceleration, then integrate

  7. Dynamics of rotational motion For rigid bodies rotating about their axis of symmetry: R m2 Second Law: m1

  8. Kinetic energy of a rigid body or an ensemble of particles Applications: rolling without slipping, combined rotational and translational motion Rotation of a rigid body about a fixed point O:

  9. Conservation laws: shortcuts to find velocities bypassing Newton’s law and accelerations • Momentum • Angular momentum • energy

  10. Work Energy Theorem

  11. does NOT depend on path!

  12. Mechanical energy is conserved! Know examples of conservative and non-conservative forces If an unknown force depends only on a coordinate, it is probably conservative

  13. Conservation of Momentum Sometimes only Fx or Fy may be equal to zero. Then only px or py is conserved. If F is not zero, but the collision is very short (Ft is small as compared to change in momentum), you can still use momentum conservation relating moments of time immediately before and after the collision. If the collision is perfectly elastic, the kinetic energy is conserved!

  14. Conservation of Angular Momentum For symmetrical objects rotating about their axis of symmetry: R m2 Second Law: m1

  15. Can be any coordinate, or angle, or anything Harmonic Motion Start from Newton’s laws Derive an equation for a small displacement from equilibrium When a force or a torque is proportional to a displacement from equilibrium, it smells like harmonic motion A and B – from initial conditions

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