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| January 14, 2016

Equation sheet When a is zero,  v is constant. ݐݒ ൅ ௢ݏൌݏ When a is constant, ଵ ൅ ݐݒ ൅ ௢ݏൌݏ ଶ ௢ݒ ଶ ൌݒ ,ݐܽ ൅ ௢ݒൌݒ ,ଶݐܽ ଶ ൅ 2ܽሺݏ െ ݏ௢ሻ, Other definition ܽ ൌ ௗ௩ ௗ௧, ݒ ൌ ௗ௦ ௗ௧, ܽൌݒ ௗ௩ ௗ௦ Velocity and acceleration in tangential normal coordinates ݒൌݒ௧݁௧, ܽൌܽ௧݁௧ ൅ ܽ௡݁௡, ൌ ܽ௧݁௧ ൅ ݒ௧߱݁௡   Where ݒ௧ ൌ ܴ߱, ܽ௧ ൌ ௗ௩೟ ௗ௧ , ߱ ൌ ௗఏ ௗ௧ Position, velocity and Acceleration in polar coordinates ݎ̅ൌ ݎ݁௥, ݒൌݒ௥݁௥ ൅ ݒఏ݁ఏ, ൌ ݒ௥݁௧ ൅ ݎ߱݁ఏ, ܽ ൌ ሺܽ௥ െ ݎ߱ଶሻ݁௥ ൅ ሺ2ݒ௥߱ ൅ ߙݎሻ݁ఏ Where ܽ௥ ൌ ௗ௩ೝ ௗ௧ , ݒ௥ ൌ ௗ௥ ௗ௧, ߱ ൌ ௗఏ ௗ௧ , ߙ ൌ ௗఠ ௗ௧ Friction force ݂ ൌ ߤܰ where N is normal force.   Forces in Cartesian coordinates ܨത ൌ ܨ௫݅൅ܨ௬݆ ൌ ݉ሺܽ௫݅൅ܽ௬݆ሻ Forces in tangential‐normal coordinates ܨത ൌ ܨ௧݁ഥ ൅ܨ ௧ ௡݁തത ௡ത ൌ ݉ሺܽ௧݁ഥ ൅ܽ ௧ ௡݁തത ௡തሻ ൌ ݉ሺ ௧ݒ݀ ݀ݐ ݁ഥ ൅ ݒ߱݁ ௧ തത ௡തሻ Forces in Polar coordinates ܨത ൌ ܨ௥݁ഥ ൅ܨ ௥ ఏത݁ത ఏത ൌ ݉ሺܽ௥݁ഥ ൅ܽ ௥ ఏത݁ത ఏതሻ ൌ ݉ሾ൬ ௥ݒ݀ ݀ݐ െ ݎ߱ଶ൰ ݁ഥ ൅௥ ሺ2ݒ௥߱ ൅ ߙݎሻത݁ത ఏതሿ Spring force ܨ௦௣ ൌ ݇∆݇ Work‐KE method ܧܭ∆ ൌ ݔ்݀ܨ න Momentum method ݒ∆݉ ൌ ݐ்݀ܨ ൌ න ܫ Average impulsive force ܨ௔௩௚ ൌ 1 ݐଶ െ ݐଵ ݐ்݀ܨ න Conservation of momentum ݉ଵݒଵ ൅ ݉ଶݒଶ ൌ ݉ଵݒଵ′൅݉ଶݒଶ′ Conservation of energy ܧܭଵ ൅ ܲܧଵ ൌ ܧܭଶ ൅ ܲܧଶ Unit conversion 1 mile = 1.6 km = 1600 m = 5280 ft 1 h = 60 min = 3600 sec Restitution ݁ ൌ ݒଶ′െݒଵ′ ݒଵ െ ݒଶ

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