Read Formula Sheet - Final Exam text version

Useful Formulae ­ PY 211 Midterm 2 Gravitational Acceleration at the Earth's Surface: One Dimensional Motion: Average Velocity: Instantaneous Velocity: Instantaneous Acceleration: Motion under constant acceleration in one dimension: Free Fall: Average Acceleration:

Two Dimensional Motion:

Motion under constant acceleration in two dimensions:

Projectile Motion: Range: Uniform Circular Motion: Centripetal Acceleration: Newton's Laws: 1st Law: 2nd Law: 3rd Law: Forces: Gravity: F= -mg Friction: Static: Resistive: Slow: Circular Motion: Period: Frequency: Maximum Height:

Kinetic: Fast:

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Work done constant force: W = F r cos Work done by varying force (1D): Spring Force: Fs = - kx Kinetic Energy: K = ½ mv2 Power: Potential Energy (1D): Total Mechanical Energy: Emech K + U Linear Momentum: p mv Newton's 2nd Law: General Work Done:

Work Energy Theorem: Units: 1 W = 1 J/s = 1 kg·m2/s3

Impulse-Momentum Theorem: Center of Mass: (discrete masses) (continuous)

Conservation of Linear Momentum: p1i + p2i = p1f + p2f Motion of System: Angular Speed: Angular Acceleration:

Kinematics of Constant Angular Acceleration: : : Rigid Object Rotating about Fixed Axis: s = r Moment of Inertia of a System of Particles: Moment of Inertia of Rigid Body: Rotational Kinetic Energy: Torque: Newton's 2nd Law: Total Kinetic Energy: v = r at = r

Angular Momentum: L r × p z component of angular momentum-rigid object rotating about fixed z axis: Lz = I Newton's Universal Gravitation: Kepler's Laws: 1st: Elliptical Orbits 2nd: G = 6.673 x 10-11 Nm2 / kg2 3rd:

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Gravitational Field: Gravitational Potential Energy of Earth: Total Energy of Satellite: Bound Circular: Bound Elliptical: Ellipse: Eccentricity: e = c/a

Area of Right Triangle: A = ½ x base x height Useful Constants: Mass of the Earth: 5.98 x 1024 kg

Mean Earth Radius: 6.37 x 106 m

Gravitational Constant: G = 6.67 x 10-11 N.m2/kg2 Gas Constant: R = 8.321 J/mol.K Boltzman Constant: kB = 1.38 x 10-23 J/K Density of Water at 0°C: 1000 kg/m3 Latent Heat of Fusion of Water: 3.33 x 105 J/kg Latent Heat of Vaporization: 2.26 x 106 J/kg Avogadro's number: NA = 6.022 x 1023 particles/mole

Moments of Inertia of Homogeneous Rigid Objects: Thin Hoop: Solid Sphere: Thin Rod Center Rotation: Rectangular Plate: Solid Cylinder: Thin Spherical Shell: Thin Rod End Rotation: Parallel Axis Theorem: Hollow Cylinder:

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Formula Sheet - Final Exam

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