Scioly Terms

Σ (sigma)

Add up all of something; in physics it means “the total of all forces or torques,” used because equilibrium depends on everything balancing together

ΣF = 0

All forces add up to zero; this means an object is not accelerating and is in static equilibrium

Στ = 0

All torques add up to zero; this means an object is not rotating and is balanced around its pivot

F

Force; a push or pull that can cause motion or deformation, measured in Newtons (N)

N (Newton)

The unit of force; roughly the force needed to hold a 100 g object against gravity (0.1 kg × 9.8 ≈ 0.98 N)

τ (torque)

Turning effect of a force; torque = force × distance from pivot, which explains why pushing farther from a hinge turns objects more easily

r or d (lever arm)

Distance from the pivot to where the force is applied; increasing this distance increases torque

Pivot / Fulcrum

The point about which an object rotates; torque is always measured relative to this point

MA (Mechanical Advantage)

How much a machine multiplies force; MA = output force ÷ input force

IMA (Ideal Mechanical Advantage)

Mechanical advantage with no friction; based only on distances or geometry

AMA (Actual Mechanical Advantage)

Real mechanical advantage with friction included; always less than IMA

F_in (effort force)

The force you apply to a machine; machines trade distance for reduced effort force

F_out (load force)

The force the machine applies to the load; this is the useful output

D_in (effort distance)

The distance the effort force moves; longer distances reduce needed force

D_out (load distance)

The distance the load moves; usually shorter when force is multiplied

η (efficiency)

How well a machine converts input work into output work; efficiency = useful output ÷ input

Efficiency %

Percent of work that becomes useful work; friction lowers efficiency below 100%

W (work)

Energy transferred by a force over a distance; work = force × distance

W_in

Input work; work you put into a machine

W_out

Output work; useful work done by the machine on the load

PE (potential energy)

Stored energy due to position or height; important for lifting machines

m

Mass; amount of matter in an object, measured in kilograms

g

Acceleration due to gravity; about 9.8 m/s² on Earth

h

Height; vertical distance an object is lifted

mgh

Gravitational potential energy; energy gained by lifting an object upward

KE (kinetic energy)

Energy of motion; objects only have KE when moving

½mv²

Kinetic energy formula; shows KE increases fast with speed

μ (mu)

Coefficient of friction; tells how rough a surface is

F_friction

Friction force; resists motion between surfaces in contact

N (normal force)

Support force from a surface; friction depends on this force

μ = F_friction / N

Definition of coefficient of friction; shows friction increases with surface force

Static friction

Friction that prevents motion from starting; usually larger than kinetic friction

Kinetic friction

Friction acting while surfaces slide; usually smaller than static friction

θ (theta)

Angle; often used for inclined planes to split forces into components

sinθ, cosθ

Trigonometric ratios; used to break forces into parallel and perpendicular components

Parallel component

Part of force along a surface; causes sliding on ramps

Perpendicular component

Part of force into a surface; determines normal force and friction

Σ (why it matters)

Symbols shorten ideas; learning what they mean lets you solve unfamiliar problems logically