Calculate rotational kinetic energy using moment of inertia and angular velocity, with equivalent equations and worked examples.
Author: Maurice Cotterell
Learn angular momentum formulas and conservation conditions, with worked examples for rigid bodies, orbits, and spinning systems.
The power reduction formula rewrites sin²θ as (1 – cos 2θ) / 2. Review trig identities, integral reduction formulas, and 9 worked examples.
Who Created Math? 5 Civilizations and 8 Mathematicians Shaped Mathematics Who Created Math? No single person created mathematics. Many civilizations developed it over thousands of years. Mathematics is the study of numbers, patterns, structure, space, change, and measurement. Contributors include Sumerians, Egyptians, Greeks, Indians, and Islamic scholars. When Did Mathematics Begin? Mathematical thinking began with counting marks on bones. Notched bones from Africa date back 35,000 to 20,000 years. The Ishango bone, found near the Nile headwaters in the Congo, may be more than 20,000 years old. Scholars interpret its marks as either a prime number sequence or a six-month…
The SI unit for electric potential is the volt (V), where 1 V = 1 J/C. The volt also measures potential difference, which is called voltage. In SI base…
The SI unit of momentum is the kilogram meter per second (kg·m/s), which equals the newton second (N·s). The CGS unit is the gram centimeter…
The electric potential energy formula for 2 point charges is U = kq₁q₂/r, where k = 8.99 × 10⁹ N·m²/C². The SI unit is the joule….
Net force is the vector sum of all forces acting on an object. The net force formula is F_net = ma, and the SI unit is the newton. A net force of zero…
Newton's Third Law States That Two Interacting Objects Exert Equal and Opposite Forces on Each Other Newton's third law is the law of action and reaction in classical mechanics. It describes every force as an interaction between 2 objects.For a standard reference, see the relevant OpenStax or College Board explanation. What Is Newton's Third Law of Motion? Two interacting objects exert forces on each other that have the same magnitude and point in opposite directions. The law is also called the law of action and reaction or the third law of motion. Action-reaction pairs appear in many systems. Examples include…
Learn conservation of momentum, when it applies, and how to solve collision problems using formulas, conditions, and worked examples.
