Questions and Answers
What is the equation for Kinematics for final velocity?
What is the equation for Kinematics for final position?
What is the equation for Kinematics for final velocity squared?
What is the equation for Net force?
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What is the equation for Impulse?
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What is the equation for Momentum?
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What is the equation for Friction?
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What is the equation for Work integral?
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What is the equation for Kinetic Energy?
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What is the equation for Gravitational Potential Energy?
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What is the equation for Coulomb's Law?
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Define Kinematics for final velocity.
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Define Kinematics for final position.
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Define Kinematics for final velocity squared.
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Define Impulse.
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Define Momentum.
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Define Friction.
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Define Work integral.
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Define Kinetic Energy.
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Define Gravitational Potential Energy.
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Define Coulomb's Law.
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Study Notes
Kinematics
- Final velocity equation: ( v = v_0 + at )
- Final position equation: ( x = x_0 + v_0 t + \frac{1}{2} at^2 )
- Final velocity squared: ( v^2 = v_0^2 + 2a(x - x_0) )
Forces and Motion
- Net force: ( \sum F = F_{\text{net}} = ma )
- Impulse as integral of force over time: ( J = \int F dt = \Delta p )
- Momentum: ( p = mv )
- Frictional force: ( F_{\text{fric}} \leq \mu N )
Work and Energy
- Work as integral of force along a path: ( W = \int F \cdot dr )
- Kinetic energy: ( K = \frac{1}{2} mv^2 )
- Power related to work: ( P = \frac{dW}{dt} )
- Power as dot product of force and velocity: ( P = F \cdot v )
- Gravitational potential energy: ( \Delta U_g = mgh )
Rotational Motion
- Centripetal acceleration: ( a_c = \frac{v^2}{r} = \omega^2 r )
- Torque: ( \tau = r \times F )
- Net torque: ( \Sigma \tau = \tau_{\text{net}} = I \alpha )
- Rotational inertia: ( I = \int r^2 dm = \Sigma mr^2 )
- Center of mass: ( r_{\text{cm}} = \frac{\sum mr}{\sum m} )
Angular Motion
- Translational velocity in terms of angular velocity: ( v = r \omega )
- Angular momentum: ( L = r \times p = I \omega )
- Rotational kinetic energy: ( K = \frac{1}{2} I \omega^2 )
- Rotational kinematics for final velocity: ( \omega = \omega_0 + \alpha t )
- Rotational kinematics for final position: ( \theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2 )
Oscillations and Law of Springs
- Hooke's law for springs: ( F_s = -kx )
- Elastic potential energy in springs: ( U_s = \frac{1}{2} kx^2 )
- General period of oscillation: ( T = \frac{2\pi}{\omega} = \frac{1}{f} )
- Period of a spring: ( T_s = 2\pi \sqrt{\frac{m}{k}} )
- Period of a pendulum: ( T_p = 2\pi \sqrt{\frac{l}{g}} )
Gravitation
- Gravitational force: ( F_g = -\frac{G m_1 m_2}{r^2} \hat{r} )
- General gravitational potential energy: ( U_g = -\frac{G m_1 m_2}{r} )
Electrostatics
- Coulomb's law: ( F = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2} )
- Electric field: ( E = \frac{F}{q} )
- Charge-line integral: ( \oint E \cdot dA = \frac{Q}{\epsilon_0} )
- Differential for electric field: ( E = -\frac{dV}{dr} )
- Electric potential: ( V = \frac{1}{4 \pi \epsilon_0} \sum_i \frac{q_i}{r_i} )
- Electric potential energy: ( U_E = qV = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r} )
Capacitance
- Capacitance relationship: ( C = \frac{Q}{V} )
- Capacitance with dielectric: ( C = \kappa \epsilon_0 \frac{A}{d} )
- Parallel capacitance: ( C_p = \sum_i C_i )
- Capacitance in series: ( \frac{1}{C_s} = \sum_i \frac{1}{C_i} )
- Energy stored in a capacitor: ( U_c = \frac{1}{2} QV = \frac{1}{2} CV^2 )
Current and Resistance
- Current differential: ( I = \frac{dQ}{dt} )
- Resistance formula: ( R = \rho \frac{l}{A} )
- Electric field related to resistivity: ( E = \rho J )
- Current: ( I = Ne v A )
Circuit Laws
- Electric potential simplified: ( V = IR )
- Resistance in series: ( R_s = \sum_i R_i )
- Resistance in parallel: ( \frac{1}{R_p} = \sum_i \frac{1}{R_i} )
- Power in electric circuits: ( P = IV )
Magnetism
- Magnetic force equation: ( F_m = q v \times B )
- Ampere's law: ( \oint B \cdot dl = \mu_0 I )
- Biot-Savart law for magnetic field: ( dB = \frac{\mu_0}{4\pi} \frac{Idl \times r}{r^3} )
- Force on current in a magnetic field: ( F = \int I dl \times B )
- Magnetic field for a series of wires: ( B_s = \mu_0 n I )
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