https://teddyrookbook.com/physics/physics-1/Recent content in Physics 1: Motion, Forces and Energy on Teddy Rook Bookhttps://teddyrookbook.com/img/share.jpghttps://teddyrookbook.com/img/share.jpgHugoenhttps://teddyrookbook.com/physics/physics-1/dimensional-analysis/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/dimensional-analysis/Every term in a physics equation must have the same units, which catches many mistakes before they happen. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/position-displacement/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/position-displacement/Pick an origin and a positive direction; displacement Δx = x_final − x_initial carries a sign. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/average-velocity/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/average-velocity/Average velocity is Δx/Δt, with a sign; average speed uses total distance instead. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/position-time-graphs/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/position-time-graphs/The slope of an x–t graph is the velocity. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/instantaneous-velocity/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/instantaneous-velocity/The velocity at an instant is the slope of the tangent line to the x–t graph. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/acceleration/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/acceleration/a = Δv/Δt; an object slows down when its acceleration points opposite to its velocity. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/velocity-time-graphs/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/velocity-time-graphs/On a v–t graph the slope is the acceleration and the area under the line is the displacement. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/motion-graph-translation/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/motion-graph-translation/Turn an x–t graph into v–t and a–t graphs, and back again. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/kinematic-equations/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/kinematic-equations/v = v₀ + at and x = x₀ + v₀t + ½at² hold when the acceleration is constant. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/kinematics-without-time/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/kinematics-without-time/v² = v₀² + 2aΔx links speeds and displacement when the time isn't known. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/free-fall/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/free-fall/Without air resistance, every dropped object speeds up by 9.8 m/s each second, whatever its mass. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/vertical-launch/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/vertical-launch/Going up, at the top and coming down, the acceleration is the same 9.8 m/s² downward. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/vector-components/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/vector-components/Split a vector into x- and y-components with sine and cosine. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/vector-addition/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/vector-addition/Add the x-parts and the y-parts, then find the size and direction of the result. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/relative-velocity/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/relative-velocity/Velocities add as vectors when you change reference frames: boats in rivers, planes in wind. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/projectile-horizontal/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/projectile-horizontal/Horizontal motion stays steady while vertical motion is free fall, and both share the same time. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/projectile-angled/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/projectile-angled/Split the launch velocity into parts, treat each direction on its own, and use the symmetry of the path. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/systems-center-of-mass/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/systems-center-of-mass/Choose what is in your system; its center of mass is the mass-weighted average position. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/free-body-diagrams/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/free-body-diagrams/Draw every force on one object as an arrow from its center, naming what exerts it. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/newtons-third-law/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/newtons-third-law/The two forces of a pair act on different objects, are the same type and are equal in size. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/equilibrium-first-law/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/equilibrium-first-law/Zero net force means constant velocity, and standing still is the special case where that velocity is zero. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/second-law-systems/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/second-law-systems/Add the forces along an axis with signs, then a = ΣF/m. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/normal-force/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/normal-force/A surface pushes as hard as it must; in an accelerating elevator the scale reading differs from mg. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/forces-at-angles/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/forces-at-angles/Resolve each force into components; the x and y directions each obey Newton's second law separately. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/inclined-planes/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/inclined-planes/On a ramp at angle θ, gravity splits into mg sin θ along the slope and mg cos θ into it. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/kinetic-friction/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/kinetic-friction/A sliding object feels friction f_k = μ_k N against its sliding. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/static-friction/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/static-friction/Static friction matches the push up to a limit of μ_s N; beyond that, the object slides. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/friction-on-inclines/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/friction-on-inclines/Find the angle where a block starts to slip, tan θ = μ_s, and its acceleration once it slides. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/connected-objects/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/connected-objects/Treat linked objects as one system to find a, then one object alone to find the tension. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/pulley-systems/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/pulley-systems/A light rope over a light pulley has one tension, and the whole system speeds up together. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/spring-force/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/spring-force/A stretched or squeezed spring pushes back with F = kx, in proportion to how far it is stretched or squeezed. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/gravitational-force/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/gravitational-force/F = Gm₁m₂/r², with r measured between the centers. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/gravitational-field/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/gravitational-field/g = GM/r² is the gravitational force on each kilogram near a planet. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/centripetal-acceleration/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/centripetal-acceleration/Moving in a circle at steady speed means accelerating toward the center: a = v²/r. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/centripetal-force/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/centripetal-force/A real force such as tension, friction or gravity supplies the net inward force mv²/r. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/vertical-circles/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/vertical-circles/At the top and bottom of a loop or a dip, the net force toward the center is mv²/r. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/work/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/work/W = Fd cos θ, and a force at right angles to the motion does no work. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/work-from-graphs/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/work-from-graphs/The area under a force–position graph is the work done. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/work-energy-theorem/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/work-energy-theorem/The net work done on an object equals its change in kinetic energy. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/potential-energy-systems/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/potential-energy-systems/ΔU = mgΔh belongs to the Earth–object system, and only changes in it matter. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/spring-potential-energy/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/spring-potential-energy/A spring stretched or squeezed by x stores ½kx². Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/energy-conservation/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/energy-conservation/When only gravity and springs do work, K + U stays the same. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/energy-bar-charts/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/energy-bar-charts/Show the energy at the start, the energy that crosses the system boundary, and the energy at the end. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/friction-energy/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/friction-energy/Friction turns mechanical energy into thermal energy: ΔE_thermal = f_k d. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/power/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/power/Power is the rate of energy transfer: P = W/Δt = Fv. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/gravitational-pe-universal/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/gravitational-pe-universal/U = −Gm₁m₂/r, which is zero when the objects are infinitely far apart. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/momentum/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/momentum/Momentum p = mv is a vector, and a system's momentum is the vector sum of its parts. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/impulse/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/impulse/FΔt = Δp, and the area under a force–time graph is the impulse. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/momentum-conservation/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/momentum-conservation/With no net outside force, the total momentum of a system stays the same. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/inelastic-collisions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/inelastic-collisions/Objects that stick move off together: m₁v₁ + m₂v₂ = (m₁ + m₂)v. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/elastic-collisions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/elastic-collisions/Kinetic energy is conserved only in elastic collisions; compare K before and after to classify one. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/explosions-recoil/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/explosions-recoil/Pieces that start at rest fly apart with equal and opposite momenta. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/center-of-mass-motion/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/center-of-mass-motion/With no outside force, a system's center of mass keeps moving at a steady velocity. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/angular-quantities/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/angular-quantities/Measure turning in radians: ω = Δθ/Δt and α = Δω/Δt. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/rotational-kinematics/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/rotational-kinematics/ω = ω₀ + αt and θ = ω₀t + ½αt² mirror the straight-line equations. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/linear-angular/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/linear-angular/A point at radius r moves with v = rω and tangential acceleration a = rα. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/torque/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/torque/Torque is a force times its lever arm: τ = rF sin θ. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/rotational-equilibrium/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/rotational-equilibrium/A balanced object has zero net force and zero net torque about any point you choose. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/rotational-inertia/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/rotational-inertia/I = Σmr²: mass far from the axis makes an object harder to spin. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/rotational-second-law/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/rotational-second-law/The net torque equals Iα. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/rotation-translation/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/rotation-translation/Solve a hanging mass on a heavy pulley with τ = Iα and F = ma together. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/rotational-kinetic-energy/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/rotational-kinetic-energy/A spinning object stores ½Iω², and a torque turning it through Δθ does work τΔθ. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/rolling/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/rolling/A rolling object shares its energy between moving and spinning, so a hoop rolls down a ramp more slowly than a ball. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/angular-momentum/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/angular-momentum/L = Iω for a spinning object and L = mvr⊥ for a passing point mass; a torque acting for a time changes L by τΔt. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/angular-momentum-conservation/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/angular-momentum-conservation/With no outside torque Iω stays the same, so a skater who pulls in her arms spins faster. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/orbiting-satellites/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/orbiting-satellites/Gravity supplies the centripetal force, so v = √(GM/r) and lower orbits are faster. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/shm-intro/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/shm-intro/A restoring force proportional to displacement makes motion repeat with a fixed amplitude, period and frequency. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/spring-oscillator-period/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/spring-oscillator-period/T = 2π√(m/k), whatever the amplitude. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/pendulum-period/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/pendulum-period/For small swings T = 2π√(L/g), and the mass of the bob doesn't matter. Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/shm-energy/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/shm-energy/Energy swaps between ½kx² and ½mv², and the total is ½kA². Physics 1: Motion, Forces and Energy · Physics Ladderhttps://teddyrookbook.com/physics/physics-1/shm-graphs/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/physics-1/shm-graphs/Position, velocity and acceleration follow sine and cosine curves, each a quarter cycle apart. Physics 1: Motion, Forces and Energy · Physics Ladder