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formulas - General Formula Sheet for PHY 53 Kinematics...

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General Formula Sheet for PHY 53 Kinematics Constant acceleration: r = r 0 + v 0 t + 1 2 a t 2 , v = v 0 + a t , v 2 = v 0 2 + 2 a ! ( r " r 0 ) Circular motion: a r = v 2 / R = R ! 2 , v = R ! Dynamics Gravitational force: F g = m g Elastic force (Hooke’s Law): F = ! kx Friction: f k = μ k N , f s ! μ s N Effective gravity: g eff = g ! a Potential Energy Gravity near earth’s surface: U = mgy Elastic force: U = 1 2 kx 2 Rotational motion and rigid bodies Circular motion in vectors: v = ! " r Radial acceleration: a r = ! " 2 r Tangential acceleration: a t = ! " r Rotational kinetic energy: K rot = 1 2 I ! 2 Symmetric bodies: ! = I " , L = I ! Rolling: v CM = R ! , a CM = R ! Oscillations (SHM) Displacement: x ( t ) = A cos( ! t + " ) Force: F = ! m " 2 x Potential energy: U = 1 2 m ! 2 x 2 Total energy: E = 1 2 m ! 2 A 2 Mass on ideal spring: ! = k / m Gravity and satellite motion Spherically symmetric object of mass M with point mass m outside at distance r from center: F = GMm r 2 , U = ! GMm r
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Energy of mass M with satellite of mass m in orbit of semi-major axis a : E = ! GMm 2 a Wave motion Harmonic wave: y ( x , t ) = A cos( kx ! " t + # ) Notation: k = 2 ! / " , ! = 2 " f , v = f ! = " / k Loudness: ! = 10log 10 ( I / I 0 ) Interference, waves of equal amplitude and intensity I 0 : I = 2 I 0 (1 + cos ! ) Phase difference only due to path difference ! x : ! = k " x Doppler effect (source chasing
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