5-Physics-Kinetics-Motion Types-Rotation

rotation as motion

Motion can be through angle around point or axis {rotation, motion}.

comparison

All linear distance, velocity, acceleration, and time relations are true for angular counterparts.

vectors

Angular quantities are vectors, perpendicular to curve plane. If right-hand fingers point in motion direction, vector points in thumb direction.

examples

Top, gyroscope, wheel, gears, banked track, and airplane dive and turn illustrate angular motion.

universe

Rotation is not relative but is absolute against distant-galaxy and universe reference frame.

spin

Motions {spin, object}| can be around object axis or point.

revolution as rotation

Objects can move around points or axes {revolution, physics}| {orbit, revolution}. Object comes back to starting point after angle 360 degrees (2*pi radians), after traveling circumference distance.

uniform circular motion

Speed can be constant around circumference {uniform circular motion}|.

angular acceleration

Angular speed w and/or direction can change over time t {angular acceleration}|: a = dw / dt. Angular acceleration a depends on angle A passed per second per second: a = (d^2)A / dt^2, where (d^2) is second derivative, and d is derivative.

angular distance

Angle distance {angular distance}| {total angle} A equals current angular distance A0 plus current angular velocity w times time t plus one-half times angular acceleration aa times time t squared: A = A0 + w * t + 0.5 * aa * t^2, whish is analogous to linear distance equation.

angular velocity

Rotation velocity {angular velocity}| w, in radians per second, is angle change A per time unit t: w = dA / dt. Average angular velocity w equals 360 degrees (2*pi radians) divided by period T: w = 2 * pi / T. Average angular velocity w equals 360 degrees (2*pi radians) times frequency f: w = 2 * pi * f.

frequency in kinetics

A number of orbits or revolutions happens over time {frequency, physics}|. Frequency f is period-T reciprocal: f = 1/T. For example, electric current alternates at 60 cycles per second in USA.

radial acceleration

Acceleration {radial acceleration}| can be along perpendicular to curve. For circular motion, object pulls back toward center to make circle, and radial acceleration ar equals tangential velocity vt squared divided by radius r: ar = vt^2 / r. If radial acceleration is more, orbit is ellipse. If radial acceleration is less, orbit is spiral.

radial velocity

Motions {radial velocity}| can be along perpendiculars to curves. Radial velocity equals zero for circular motion, because distance from circle center is constant.

rotation period

If object rotates around point or axis, object makes one complete revolution during time {period, rotation} {rotation period}|. Complete revolution sweeps through angle of 360 degrees (2*pi radians) and travels circumference distance. Period T is frequency f reciprocal: T = 1/f.

tangential acceleration

Acceleration {tangential acceleration}| can be along tangent to curve. Tangential acceleration at equals angular acceleration a times curvature radius r: at = a * r.

tangential velocity

Motions {tangential velocity}| can be along tangents to curves. Tangential velocity vt equals angular velocity w times curvature radius r: vt = w * r.