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Symmetry and Newton’s Laws

Symmetry and Newton’s Laws. Mr Finn Honors Physics (2012). Newton’s 1 st Law. Galileo’s Law of Inertia = N1L “All objects retain their state of motion, whether at rest or uniform velocity, in the absence of external (unbalanced) forces.”

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Symmetry and Newton’s Laws

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  1. Symmetry and Newton’s Laws Mr Finn Honors Physics (2012)

  2. Newton’s 1st Law • Galileo’s Law of Inertia = N1L • “All objects retain their state of motion, whether at rest or uniform velocity, in the absence of external (unbalanced) forces.” • Inertial Frame of Reference (IFoR): any FoR within which N1L is true • IFoR move at constant velocity relative to each other • Non-inertial Frame of Reference (NFoR): FoR within which N1L is not true • NFoR accelerate relative to IFoR

  3. Two Inertial Frames of Reference FoR1 FoR2 z2 z1 U(2/1) = velocity of FoR2 relative to FoR1 A x2 x1 y2 y1 U(2/1) = - U(1/2) = u

  4. Galilean Transformation • How to describe the position of object A relative to two IFoR? • x(A/2) = x-position of A relative to FoR2 = x(A/1) – u t • y(A/2) = y(A/1) • z(A/2) = z(A/1) • t(2) = t(1) or time is the same in both FoR (classically) • Simplify notation: • x2 = x1 – u t • y2 = y1 • z2 = z1 • t2 = t1 = t

  5. Newton’s 2nd Law • Verbal: • An object changes its state of motion (accelerates) in direct proportion to the net force acting upon it, in inverse proportion to its inertia (mass), and in the direction of the net force. • Mathematical: • where the acceleration is measured relative to IFoR, net force is vector sum of all forces acting on object, acceleration vector is parallel to the net force vector

  6. N2L in Two IFoR • Compare Newton 2nd Law in two inertial FoR • acceleration: how does acceleration compare when measured in different IFoR? • inertia/mass: how does the inertia of an object compare in two different IFoR? • net Force: how does the force acting on an object compare in two different IFoR?

  7. Velocity & Acceleration • Velocity relative to two IFoR • v2x= velocity of object A relative to FoR2 in x-direction • v2y = v1y and v2z = v1z • Acceleration relative to two IFoR • a2x = acceleration of object A relative to FoR2 in x-direction • a2y = a1y and a2z = a1z

  8. Inertia • Mass or inertia is the same in both FoR • Classically, inertia/mass does not depend on • position • velocity

  9. Forces • Interactions between objects depend on: • distance between objects (same in all FoR) • inherent properties of objects (inherent – independent of FoR) • Classification of forces • gravity: mass, distance between objects • normal: compression of object (change in size) • tension: stretching of object (change in size) • friction: surface properties, normal force, motion or not between surfaces • drag: size/shape of object, speed relative to air, density of air • speed is relative to medium/air, not FoR • All forces are the same • vector sum of forces = same

  10. Symmetry • Galilean transformation: describe motion of object from two different IFoR no change in N2L • same acceleration • same inertia/mass • same force/net force • Rotate equilateral triangle by 120°, 240°, 360°, flip on axes  no change in triangle • Symmetry = change PoV, object is the same

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