Formula Sheet - Final Exam

Gravitational Acceleration at the Earth’s Surface:One Dimensional Motion:Useful Formulae – PY 211 Midterm 2Average Velocity:Average Acceleration:Instantaneous Velocity:Instantaneous Acceleration:Motion under constant acceleration in one dimension:Free Fall:Two Dimensional Motion:Motion under constant acceleration in two dimensions:Projectile Motion:Range:Maximum Height:Uniform Circular Motion:Centripetal Acceleration: Period: Frequency:Newton’s Laws:1 st Law:2 nd Law: Circular Motion:3 rd Law:Forces: Gravity: F= -mgFriction: Static:Resistive: Slow:Kinetic:Fast:1

Work done constant force: W = F Δr cos θWork done by varying force (1D):Spring Force: F s= - kxKinetic Energy: K = ½ mv 2Work Energy Theorem:General Work Done:Power: Units: 1 W = 1 J/s = 1 kg·m 2 /s 3Potential Energy (1D):Total Mechanical Energy: E mech ≡ K + ULinear Momentum: p ≡ mv Newton’s 2 nd Law:Impulse-Momentum Theorem:Center of Mass: (discrete masses)(continuous)Conservation of Linear Momentum: p 1i + p 2i = p 1f + p 2fMotion of System:Angular Speed:Angular Acceleration:Kinematics of Constant Angular Acceleration:: :Rigid Object Rotating about Fixed Axis: s = rθ v = rω a t = rαMoment of Inertia of a System of Particles:Moment of Inertia of Rigid Body:Rotational Kinetic Energy:Total Kinetic Energy:Torque:Newton’s 2 nd Law:Angular Momentum: L ≡ r × pz component of angular momentum-rigid object rotating about fixed z axis: L z = IωNewton’s Universal Gravitation: G = 6.673 x 10 -11 Nm 2 / kg 2Kepler’s Laws: 1 st : Elliptical Orbits 2 nd : 3 rd :2

Gravitational Field:Gravitational Potential Energy of Earth:Total Energy of Satellite:Bound Circular:Bound Elliptical:Ellipse:Eccentricity: e = c/aArea of Right Triangle: A = ½ x base x heightUseful Constants:Mass of the Earth: 5.98 x 10 24 kgMean Earth Radius: 6.37 x 10 6 mGravitational Constant: G = 6.67 x 10 -11 N . m 2 /kg 2Gas Constant: R = 8.321 J/mol . KBoltzman Constant: k B = 1.38 x 10 -23 J/KAvogadro’s number: N A = 6.022 x 10 23 particles/moleDensity of Water at 0°C: 1000 kg/m 3Latent Heat of Fusion of Water: 3.33 x 10 5 J/kgLatent Heat of Vaporization: 2.26 x 10 6 J/kgMoments of Inertia of Homogeneous Rigid Objects:Thin Hoop: Solid Cylinder: Hollow Cylinder:Solid Sphere:Thin Spherical Shell:Thin Rod Center Rotation:Thin Rod End Rotation:Rectangular Plate:Parallel Axis Theorem:3