Mechanics & Energy

Mechanical Advantage of Pulley Systems

"Movable Pulleys Multiply, Fixed Pulleys Fix Direction"

Example:

A system with 3 movable pulleys has MA = 3

Adding fixed pulleys changes direction but MA stays the same

Combustion & Chemical Energy Release

"Break High, Make Low — Energy Will Flow"

Break high-energy bonds

Make low-energy bonds

Then energy is released

Spring Potential Energy

"Spring Energy is Half K X-Squared"

Power in Translational Motion

"Power Flows from Force and Speed"

Torque Direction & Sign Convention

"Counter is Positive — Clock is Not"

Translational Kinetic Energy

The energy of an object due to its motion in a straight line (translation through space).

Static Rotational Equilibrium

No Torque, No Twist

A state where an object is not rotating or rotating at a constant angular velocity, with no net torque acting on it.

Gravity - Conservative Force

Gravity's Work is Path-Free

A conservative force is a force where the work done moving an object between two points is independent of the path taken.

Derived vs. SI Base Units

“Big Seven Make the Rest Happen"

Base SI Units:

The fundamental units defined by the International System of Units (SI) from which all other units are derived.

Examples:

Length → meter (m)

Mass → kilogram (kg)

Time → second (s)

Electric current → ampere (A)

Temperature → kelvin (K)

Amount of substance → mole (mol)

Luminous intensity → candela (cd)

Derived Units:

Units built from base units using multiplication or division.

Examples:

Newton (N) = kg·m/s² (for force)

Joule (J) = kg·m²/s² (for energy)

Pascal (Pa) = N/m² = kg/m·s² (for pressure)

Mechanical Advantage

"Machines Amplify"

Mechanical Advantage is a measure of how much a machine multiplies input force to make work easier.

Static vs. Kinetic Friction

“Static Stops, Kinetic Keeps Sliding"

Static = Sticking

Kinetic = Keeps moving

Torque and the Sine Function

Sine Spins Strongest at 90

Torque is strongest when the force is perpendicular to the lever arm

Mechanical Advantage of a Lever

The mechanical advantage (MA) of a lever is how much the lever amplifies the input force to move a load.

Work

Work = Force × Distance × Cosine

Work is done when a force causes displacement of an object in the direction of the force.

Weight

Weight Means Gravity

The force due to gravity acting on an object's mass.

Tough Rotations Require Force and Radius

A measure of how much a force causes an object to rotate around an axis.

Conservation of Total Energy

Energy Can Change Clothes, But Never Leaves the Party

The total energy of an isolated system remains constant—it can change forms (e.g., kinetic ↔ potential), but cannot be created or destroyed.

Gravitational Potential Energy

U Might Go High

The energy an object has due to its position above the ground in a gravitational field

Heat of Fusion

"Heat of fusion is the quiet power that melts a solid—without making it hotter, just looser."

Snell’s Law (Law of Refraction)

“Snell’s Law says light changes its stride—bending its path to match the ride."

Law of Reflection (“In = Out, Angle by Angle!”)

States that the angle of incidence (incoming ray) equals the angle of reflection (outgoing ray) on smooth surfaces

Doppler Effect (“Closer = Higher, Farther = Lower”)

The change in frequency or wavelength of a wave (sound, light, etc.) when the source or observer is moving relative to the other

Elastic Force & Equilibrium

• Stretch it, it pulls back

• Compress it, it pushes out

  
  Elastic force always acts toward the equilibrium position

Electric Force in an Electric Field

"Electric fields whisper a push to any nearby charge—just multiply and feel the nudge."

Place a charge in a field—force pops out directly from the combo of q and E

Force in Direction of Motion

When net force acts in the same direction as an object’s motion, it causes the object to accelerate (speed up)

Kinetic Energy and Speed Relationship

"When energy leaps twice as high, speed grows by root two—not sky high."

Period (T)

“Time for One Turn = T”

Frequency–Period Formula

“Flip the F and T!”

They're reciprocals—each defines how fast or slow cycles occur

Velocity Equation (Average Speed)

“D Over T Is How Fast You’ll Be!”

Circumference of a Circle

“2πR Rolls the Rim”

Finding Period (T) Using Circumference and Speed

"Period is how long it takes to loop the circle once—distance around divided by speed you roll."