MCAT Physics - Kinematics and Dynamics

British/Imperial/Foot-Pound-Second (FPS) system

standardized system of measurement typically only used in the US

foot (ft)

Imperial unit of length

pound (lb)

Imperial unit of weight

second (s)

Imperial/SI unit for time

slug

Imperial unit for mass

Metric/Meter-Kilogram-Seconds (MKS)/Centimeters-Grams-Seconds (CGS) system

most common system of units

System International (SI) units

units system used in science worldwide

meter (m)

SI unit for length

kilogram (kg)

SI unit for mass

ampere (A)

SI unit for current, equal to coulomb/second

mole (mol)

SI unit for amount of subtance

kelvin (K)

SI unit for temperature

candela (cd)

SI unit for luminous intensity

base units

standard units around which the system is designed

derived units

units created by associating base units

newton (N)

SI unit of force; equal to 1 kg*m/s²

joule (J)

Unit of work and energy; equal to 1 kg*m²/s²

watt (W)

Unit of power; equal to 1 kg*m²/s³

ångström (Å)

unit of length on atomic scale; equal to 10^-10 m

electron-volt (eV)

unit of energy on atomic scale; equal to 1.6 × 10^-19 J

vector

number with magnitude and direction; represented by arrow or bold; magnitude uses absolute value lines or italics

scalar

number with magnitude only

vector quantities

displacement, velocity, acceleration, force

scalar quantities

distance, speed, energy, pressure, mass

resultant

the sum or difference of two vectors

tip-to-tail method

method of illustrating vector addition

components

properties of vectors described by dividing vectors by unit perpendicular lines

vector subtraction

A - B = A + -B; adding a vector with same magnitude but opposite direction

Multiplying vector by scalar

multiply magnitude of vector by absolute value of n, then adjust direction based on sign

dot product

A · B = |A| |B| cos θ; generates scalar quantity

cross product

A × B = |A| |B| sin θ; generates vector (equation produces magnitude, right-hand rule produces direction)

right-hand rule

hand towards A, curl towards B, thumb is C/resultant

displacement (x/d)

change in position in space; vector that connects initial and final position; doesn’t consider path; m

distance (d)

considers path taken, scalar, m

velocity (v)

rate of change of displacement in a given time; same direction as displacement; m/s

speed (v)

rate of actual distance in a given time, m/s

instantaneous velocity/speed

average velocity as change in time approaches 0; scalar

delta (Δ)

change in

Force (F)

vector quantity experienced as attraction or repulsion; N

Gravity

attractive force felt by matter

gravitational force equation

F_g= Gm₁m₂/r²

universal gravitational constant (G)

6.67 × 10^-11 N*m²/kg²

gravitational acceleration (g)

near Earth’s surface; 9.81 m/s²

Friction

type of force that opposes the movement of objects

Static friction (f_s)

friction between a stationary object and the surface upon which it rests; 0 ≤ f_s ≤ μ_sN

coefficient of friction (μ)

unitless quantity that is dependent on the two materials in contact, μ_{s >} μ_k

normal force

component of the force between two objects in contact that is perpendicular to the plane of contact

Kinetic friction (f_k)

friction between a sliding object and the surface over which the object slides; f_k = μ_kN

Mass (m)

measure of a body’s inertia, the amount of matter in the object; kg

weight (F_g)

measure of gravitational force on an object’s mass; F_g = mg

center of mass/gravity

a single point to which weight is applied in an object; in each coordinate, equal to the sum of mass times position divided by the sum of mass; the center of mass of a uniform object is at the geometric center of the object

acceleration (a)

rate of change of velocity that an object experiences as a result of some applied force; m/s²

deceleration

acceleration in the direction opposite the initial velocity

Newton’s FIrst Law of Motion/Law of Inertia

A body either at rest or in motion with constant velocity will remain that way unless a net force acts upon it; F_net = ma = 0

Newton’s Second Law of Motion

An object of mass m will accelerate when the vector sum of the forces results in some nonzero resultant force vector; F_net = ma

Newton’s Third Law of Motion/Law of Action and Reaction

To every action, there is always an opposed but equal reaction; F_AB = -F_BA

Linear motion

the pathway of the moving object continues along a straight line

Linear kinetics equation - no x

v = v₀ + at

Linear kinetics equation - no v₀

x = vt - ½ at²

Linear kinetics equation - no v

x = v₀t + ½ at²

Linear kinetics equation - no a

x = ½(v₀ + v)t

Linear kinetics equation - no t

v² = v₀² + 2ax

vertical motion

use y in place of x

terminal velocity

maximum velocity due to drag force equally weight of falling object

free fall

vertical motion without regard to air resistance

Air resistance

friction-like force that opposes a falling object; increases with speed

drag force

force of air resistance; eventually equals weight of object to result in terminal velocity

projectile motion

motion that follows a path along two dimensions; to solve, divide motion into components

inclined planes

ramps; to solve problems, divide forces into components

circular motion

forces cause an object to move in a circular pathway; Upon completion of one cycle, the displacement of the object is zero

uniform circular motion

instantaneous velocity vector is always tangent to circular path

centripetal force

keeps object moving circularly; points radially inwards; F_c = mv²/r

dynamics

study of forces and torques

free body diagrams

a graphical illustration used to visualize the applied forces, moments, and resulting reactions on a body in a given condition

transitional equilibrium

motion without rotation

first condition of equilibrium

when the vector sum of all of the forces acting on an object is zero, a reiteration of Newton’s first law

rotational equilibrium

occurs when forces are applied against an object in such a way as to cause the object to rotate around a fixed pivot point

fulcrum

a fixed pivot point

torque/moment of force (τ)

generated by application of force at some distance from the fulcrum; τ = r × F = rF sin θ

lever arm

the distance between the applied force and the fulcrum

second condition of equilibrium

when the vector sum of all the torques acting on an object is zero