Motion and Collisions: Impulse, Angular Velocity, and Friction
Impulse, angular velocity, elastic collisions, and the coefficient of friction — four foundational mechanics calculations.
Motion and collisions in introductory mechanics reduce to a handful of formulas — these four cover force over time, rotation, energy-conserving impacts, and surface friction.
Impulse: force applied over time
Impulse equals force times time interval. A 200 N force applied for 0.5 seconds produces an impulse of 100 N·s — equal to the resulting change in momentum, which is why impulse is often introduced alongside momentum conservation problems.
Angular velocity: rotation rate from angle and time
Angular velocity is angle rotated divided by time. Rotating a full 6.28 radians (2π, one complete revolution) in 2 seconds gives an angular velocity of 3.14 rad/s.
Elastic collisions: velocity after a perfectly bouncy impact
In a 1D elastic collision, both momentum and kinetic energy are conserved, producing specific formulas for each object's post-collision velocity based on both masses and initial velocities — unlike inelastic collisions, where kinetic energy is not conserved and objects may stick together.
Coefficient of friction: quantifying surface grip
Friction coefficient is friction force divided by normal force. A 40 N friction force against a 100 N normal force gives a coefficient of 0.4 — a value specific to the pair of surfaces in contact, not either surface alone.
The mechanics of motion, quantified
Force over time, rotation rate, collision outcomes, and surface friction are the building blocks of classical mechanics problem-solving. Try the impulse calculator, angular velocity calculator, elastic collision calculator, and coefficient of friction calculator.