College Physics I

Units

1. 1

   Kinematics

   7 lessons

   1. Scalars and Vectors in One DimensionSet up a coordinate axis, find displacement as final minus initial, tell distance and speed from displacement and velocity, and add one-dimensional vectors as signed numbers.
   2. Displacement, Velocity, and AccelerationCompute average velocity and average acceleration, use the signs of velocity and acceleration to say whether an object speeds up or slows down, and see that velocity can be zero while acceleration is not.
   3. Position-time and velocity-time graphsRead velocity from the slope of a position-time graph, acceleration from the slope and displacement from the area of a velocity-time graph, and change from one representation to another.
   4. The kinematic equationsChoose and use v = v₀ + at, Δx = v₀t + ½at² and v² = v₀² + 2aΔx for constant acceleration, with signs and free fall, and say when they fail.
   5. Reference Frames and Relative MotionSay "relative to what" for every velocity, add signed velocities between frames, find a closing speed, and show that frames at constant relative velocity agree on acceleration.
   6. Vector componentsSplit a vector into perpendicular components with cosine and sine, add vectors by adding like components, and rebuild the magnitude and direction with the right quadrant.
   7. Projectile motionTreat the horizontal and vertical motion of a projectile separately, joined by time, to find time of flight, range, maximum height and impact velocity.
2. 2

   Force and translational dynamics

   11 lessons

   1. Systems and Center of MassChoose a system, separate internal from external forces, find a center of mass as a weighted average, and use ΣF_ext = M a_cm.
   2. Free-body diagramsDraw a free-body diagram with one arrow for every external force on one object, name the source of each arrow, and find the normal, tension and friction forces that balance at rest.
   3. Newton's third lawName the third-law partner of a force, explain why the pair has equal sizes and opposite directions, and show that the two forces never cancel because they act on different objects.
   4. Newton's first law and equilibriumState the first law, separate inertia from force, and solve equilibrium problems with ΣF_x = 0 and ΣF_y = 0, including tensions at angles.
   5. Newton's second law for one objectUse ΣF = ma with signed components for one object, tell weight from mass, and find a scale reading in an accelerating elevator.
   6. Connected objects and inclinesWrite one second-law equation for each connected object and link them with a shared acceleration and tension, then resolve weight on an incline to find acceleration with and without friction.
   7. Gravitational force and fieldsUse F = G m₁m₂ / r² and g = GM / r², scale gravity with the inverse square of the center-to-center distance, and explain weight, weightlessness and why every object falls at the same rate.
   8. Static and kinetic frictionUse f_s ≤ μ_s N and f_k = μ_k N, decide first whether an object slides, find the normal force from the perpendicular equation, and give the direction of friction from the sliding of the surfaces.
   9. Spring forces and Hooke's lawUse F_s = −kx with x measured from the natural length, read k from a force-extension graph, and explain why a mass on a spring does not have constant acceleration.
   10. Centripetal acceleration and forceFind the acceleration and the net inward force of an object moving in a circle at constant speed, say which real force supplies it, and predict what happens when it stops.
   11. Vertical circles, banked curves and orbitsApply the inward-components rule to a loop, a banked curve and a circular orbit, and find the normal force, the banking angle, and the orbital speed and period.
3. 3

   Work, energy and power

   6 lessons

   1. Kinetic energyCalculate the kinetic energy K = ½mv² of an object or a system, use its proportionality to v², and tell it apart from momentum.
   2. Work and the work-energy theoremCalculate the work of a force with W = Fd cos θ, give it the right sign, and use W_net = ΔK to find a speed or a distance.
   3. Gravitational and spring potential energyFind the change in gravitational and elastic potential energy of a system with ΔU_g = mgΔy and U_s = ½kx², and say what the zero level, the system and the path do and do not change.
   4. Energy conservation and energy bar chartsChoose a system, draw energy bar charts before and after, and use K_i + U_i + W_ext = K_f + U_f to find a speed, a height or a compression.
   5. Energy with friction and open systemsAccount for friction as thermal energy ΔE_th = f_k d, write K_i + U_i + W_ext = K_f + U_f + ΔE_th for a chosen system, and find speeds, forces and efficiencies.
   6. PowerFind average power with P = W/Δt, instantaneous power with P = Fv cos θ, and energy from a power rating, and tell power from work and energy.
4. 4

   Linear momentum

   5 lessons

   1. MomentumCalculate momentum p = mv with its sign, add the momenta of a system, and tell momentum from kinetic energy and from force.
   2. Impulse and force-time graphsUse J = FΔt = Δp to find impulse, momentum change, speed and average force, read impulse as the area under a force-time graph, and explain how a longer contact time lowers the force.
   3. Conservation of momentum and center-of-mass velocityChoose a system, write total momentum before and after with signs, solve for an unknown velocity, and say when an external impulse breaks conservation.
   4. Elastic collisionsSolve a head-on elastic collision from conservation of momentum and kinetic energy, use the approach-separation shortcut, and predict the outcomes for different mass ratios.
   5. Inelastic collisions and energy lossFind the final velocity and the kinetic energy lost in a perfectly inelastic collision, compare it with an explosion, and solve a ballistic pendulum in two stages.
5. 5

   Torque and rotational dynamics

   6 lessons

   1. Rotational kinematicsDescribe turning with angular position, velocity and acceleration in radians, and use the constant-α equations and the ω-t graph to find angles and speeds.
   2. Linking linear and rotational motionConnect the turning of a rigid object to the motion of one of its points: arc length, tangential speed, tangential and centripetal acceleration, and belts between wheels.
   3. TorqueFind the torque of a force about an axis with τ = rF sin θ, give it a sign, add torques about one axis, and say when a force gives none.
   4. Rotational inertiaFind the rotational inertia of a set of point masses about an axis with I = Σ m r², and explain how mass, its spread and the axis set the resistance to angular acceleration.
   5. Rotational equilibrium and Newton's first law in rotational formState the two conditions for static equilibrium, ΣF = 0 and Στ = 0, and use them with a well-chosen axis to find unknown forces on seesaws and hinged beams.
   6. Newton's second law in rotational formUse Στ = Iα to find the angular acceleration caused by a net torque, and solve a block hanging from a pulley that has rotational inertia.
6. 6

   Energy and momentum of rotating systems

   6 lessons

   1. Rotational kinetic energyFind the kinetic energy of a spinning object with K = ½Iω², include it in energy conservation, and add translational and rotational energy for an object that does both.
   2. Torque and workFind the work of a torque with W = τΔθ, add the works of several torques, and link the net work to the change in rotational kinetic energy.
   3. Angular momentum and angular impulseFind the angular momentum of a rigid object, L = Iω, and of a particle about a point, L = r⊥mv, and use angular impulse, τΔt = ΔL, to find how a torque changes it.
   4. Conservation of angular momentumUse L_i = L_f when no net external torque acts, to find new angular velocities when the rotational inertia changes or two objects stick, and say what happens to kinetic energy.
   5. Rolling without slippingUse v_cm = ωR for a wheel that does not slip, find the speeds of its points, and combine translational and rotational energy to find how fast rolling objects come down a ramp.
   6. Motion of orbiting satellitesUse conservation of angular momentum and of total mechanical energy to explain how a satellite's speed changes around an ellipse, and find the speed, period and energies of a circular orbit.
7. 7

   Oscillations

   4 lessons

   1. Simple harmonic motionDefine simple harmonic motion by its restoring force F = −kx, say where the force, acceleration and speed are largest in a cycle, and tell SHM systems from other repeating motion.
   2. Frequency and period of SHMFind the period and frequency of a mass on a spring and of a simple pendulum, say what each does and does not depend on, and read k or g from a straight-line graph.
   3. Representing and analyzing SHMRead amplitude, period and frequency from a position-time graph, find where velocity and acceleration are zero or greatest, and link the x-t, v-t, a-t and force-displacement graphs of one oscillator.
   4. Energy of simple harmonic oscillatorsShow that an undamped oscillator keeps a constant total energy E = ½kA², find K, U and the speed at any position, and explain what damping does.
8. 8

   Fluids

   5 lessons

   1. DensityCalculate density from mass and volume in kg/m³, find the density of a mixture, and decide whether an object floats by comparing densities.
   2. PressureUse P = F/A, find the pressure at depth in a fluid with P = P₀ + ρgh, tell gauge from absolute pressure, and use the fact that pressure acts in every direction.
   3. Buoyancy and Archimedes' principleExplain the buoyant force as a pressure difference, calculate F_B = ρ_fluid V_displaced g, and use it with Newton's second law for floating, sinking and hanging objects.
   4. The continuity equationUse the volume flow rate Q = Av and A₁v₁ = A₂v₂ to find speeds in a narrowing pipe, scale them with the radius squared, and add the flow rates at a branch.
   5. Bernoulli's equationApply P + ρgy + ½ρv² = constant along a streamline with continuity, find the pressure change in a narrowing or rising pipe, and use Torricelli's v = √(2gh) for a tank.