Fill-in-yourself formula sheet for Supplementary Physics - dirac

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Fill-in-yourself formula sheet for Supplementary Physics - dirac

Fill-in-yourself formula sheet for Supplementary PhysicsBasic kinematics in 1D: position, velocity, acceleration• Average velocity betwen times t 1 and t 2 in terms of positions x(t 2 ) and x(t 1 )• Instantaneous velocity from x(t): v(t) =• Change on position given v(t): ∆x = x(t 2 ) − x(t 1 ) =• Instantaneous acceleration from v(t): a(t) =• Change in velocity give a(t):Kinematics: constant acceleration in 1D• Change in velocity after a time t: v =• Change in position after a time t: ∆x =• Elimininating time gives a relation between change in v 2 and ∆x:Kinematics: uniform circular motion• Speed in terms of radius r and period T (time for one rotation):v =• Angular velocity ω in terms of T• Speed in terms of ω• Centripetal acceleration in terms of v and r• Centripetal acceleration in terms of ω and rDynamics: Newton’s laws and different forces• Newton’s second law• Newton’s third law• Weight force near surface of the earth: W =• General law of gravitation, the magnitude of the force on each of a pair of particles given their masses and the distancebetween them: F g• Kinetic friction: F k =• Static friction: F s ≤• Drag force: F d =• Ideal spring, for a displacement x = l − l 0 (current and natural length of spring): F(x) =Work and energy:• Kinetic energy of a particle K =• Work done by a force ⃗ F during a displacement ⃗ d• Work-kinetic energy theorem:• Work done by gravity when height changes from y 0 to y• Gravitational potential energy (hear Earth’s surface) for particle at height h above the “zero” level U g =• Potential energy stored in a spring U sp =• Power: P =1


Some problem solving tips• Draw a free-body diagram• Resolve forces if necessary• Think carefully about the direction of friction• Identify what you know and what you don’t know• If you get to a point where the number of things you don’t know is the same as the number of equations you have, thenthe rest should be just algebraMathematics: calculusddx x = 1ddx x2 = 2xddx x3 = 3x 2ddx xn = nx n−1Mathematics: geometry/trigonometryFIG 1FIG 2BACDEFθLaθ ’b∫∫∫∫dx = xxdx = x 2 /2x 2 dx = x 3 /3x n dx = x n+1 /(n + 1)In Fig 1, suppose you know angle A. Whatare all the other angles in terms of A? (forexample some are equal to A, some 180 ◦ − A)or 90 ◦ − A). Fill in the answers. For practice,make the diagram again yourself.In Fig 2., when you have a right angle triangleand you know one other angle, θ, the other oneis 90 ◦ − θ, which I usually call θ ′ Some basictrig formulas are (here θ ′ ≡ 90 ◦ − θ)Mathematics: Algebraa = L cos(θ)b = L sin(θ)tan(θ) = sin(θ)/cos(θ)sin(θ) = cos(θ ′ )cos(θ) = sin(θ ′ )• Quadratic formula, of solutions ax 2 + bx + c = 0:x = −b ± √ b 2 − 4ac2a• To eliminate unknowns which you don’t need, when you have two equations, consider dividing one equation by another,or adding them together, or subtracting one from the other.Mathematics: Calculators• Make sure you set the calculator to degree mode.• The chances of a typing error are higher than you think–check that answers look reasonable2

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