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Useful Equations: Physics 202 FORCE and MOMENTUM: Momentum: p mv (and p is conserved in the absence of external forces) Force: 2nd law: dp F dt F ma or (if mass is constant) 3rd law: FAB FBA Impulse: Impulse F dt and F dt p ENERGY: Kinetic Energy: Work: kg m 2 1 J 1 2 s K 2 mv 2 1 work F dx F x (if force is constant) Work-energy theorem: Net work F dx K Gravity: F mg (pointing down), U mgh F kx , U 2 kx 2 Ideal Springs: 1 CONSERVATIVE FORCES: Let FU FU , x iˆ FU , y ˆj FU , z kˆ dU dU dU Then FU , x , FU , y , and FU , z dx dz dy And U FU dx Physics 202 equations Page 2 ROTATION: If angular acceleration is constant, 0t 12 t 2 1 2 0 t Rotational Inertia: I m r 2 (t ) 0 t , 1 2 2f 12 i2 and for a rolling object I M R2 2 Parallel axis theorem: 𝐼𝑎𝑏𝑜𝑢𝑡 𝑎𝑛𝑦 𝑝𝑜𝑖𝑛𝑡 = 𝐼𝑎𝑏𝑜𝑢𝑡 𝑡ℎ𝑒 𝐶𝑀 + 𝑀𝑅𝐶𝑀 Kinetic Energy: Ktranslation 12 m v2 Work: Work d Angular momentum: or and Krotation 12 I 2 Work if torque is constant I (for a rigid body) or r p (always) Torque: r F if I is constant I Newton’s second law: d d r p (always) dt dt FLUIDS: Flow rate: flow rate volume velocity Area time or v dA Static Fluid Pressure: P g depth if is constant U P g y Fluid Potential: fluid potential P vol. if is constant Bernoulli’s equation (in the absence of friction): K P constant OR P g y 12 v2 constant vol. Fd kinematic viscosity Viscosity: Av Viscosity controlled flow: potential difference flow rate resistance Poisuille’s equation (hollow pipes): resistance= 8 r4 length, r radius Darcy’s equation (flow through materials): resistance= kinematic viscosity, length, permeability Area Physics 202 equations Page 3 ELECTRIC FORCES, FIELDS, AND POTENTIALS: Coulomb’s Law and Electric Fields: The magnitude of the force between point charges separated by a distance r is given by k q q 1 q1 q2 F 12 2 2 r 4 0 r The electric field is the force per unit charge, F q E . For a point charge the magnitude is given by kq E 2 r Electric Potential: The electric potential V is the potential energy per unit charge: dV dV and V E dx , Ex , Ey , etc. dx dy If we choose to set the potential of points infinitely far from charges to be zero, then the potential of a point charge is given by: kq 1 q V r 4 0 r ELECTRIC CIRCUITS: V IR Resistors (Ohm’s Law): Power: Power V I I 2 R Kirchhoff’s Rules: 1. “Current in = current out” or “ Iin 0 ” 2. Going around a closed loop, Resistors in parallel: 1 RTOTAL voltages 0 1 1 R1 R2 RTOTAL R1 R2 …in series: