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

**Fill**-**in**-**yourself** **for**mula**sheet** **for** **Supplementary** **Physics**Basic k**in**ematics **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):K**in**ematics: constant acceleration **in** 1D• Change **in** velocity after a time t: v =• Change **in** position after a time t: ∆x =• Elim**in****in**at**in**g time gives a relation between change **in** v 2 and ∆x:K**in**ematics: uni**for**m 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 **for**ces• Newton’s second law• Newton’s third law• Weight **for**ce near surface of the earth: W =• General law of gravitation, the magnitude of the **for**ce on each of a pair of particles given their masses and the distancebetween them: F g• K**in**etic friction: F k =• Static friction: F s ≤• Drag **for**ce: F d =• Ideal spr**in**g, **for** a displacement x = l − l 0 (current and natural length of spr**in**g): F(x) =Work and energy:• K**in**etic energy of a particle K =• Work done by a **for**ce ⃗ F dur**in**g a displacement ⃗ d• Work-k**in**etic 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 spr**in**g U sp =• Power: P =1

Some problem solv**in**g tips• Draw a free-body diagram• Resolve **for**ces if necessary• Th**in**k carefully about the direction of friction• Identify what you know and what you don’t know• If you get to a po**in**t where the number of th**in**gs 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? (**for**example some are equal to A, some 180 ◦ − A)or 90 ◦ − A). **Fill** **in** the answers. For practice,make the diagram aga**in** **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 ** formula**s are (here θ ′ ≡ 90 ◦ − θ)Mathematics: Algebraa = L cos(θ)b = L s