Angular velocity (ω = 2π · rpm / 60) is how fast an angle is swept out, in radians per second. Set the spin rate with the rpm slider and move the outer marker with the radius slider, then compare the two markers: they share one ω, one period and one frequency, but not one speed.
Start with the rotation rate slider, which runs from 1 to 600 rpm. Push it up and three readouts move together: ω climbs in rad/s, the frequency f climbs in hertz, and the period T falls, because a faster disc needs less time per turn. Those three are one fact in three costumes — 60 rpm is one turn per second is 6.283 rad/s is a period of exactly 1 s. The equivalent-rpm line under the ω readout converts back the other way, so you can check a conversion in either direction. For your own numbers, the angular velocity calculator solves the same relation for whichever quantity is missing.
Now leave the rpm slider alone and drag the radius slider from 0.05 m out to 1.00 m. This is the part worth watching closely. The tangential speed readout climbs steadily, the centripetal acceleration climbs far harder, and the angular velocity, period and frequency do not move by so much as a digit. That is not a rounding artefact in the lab — it is the definition of rigid-body rotation. The angle swept per second belongs to the disc, so it is the same everywhere on it, while the distance covered per second depends on how far out you are standing.
The two markers make it concrete. The inner one is pinned at exactly half the outer radius, and its speed readout is always exactly half the outer marker's, at any rpm and any radius. The velocity arrows on the canvas keep that 2:1 ratio too. That is v = ωr read off directly: same ω, half the r, half the v. The shaded sector tracks the angle swept since you last hit Reset angle, and the revolution counter accumulates past one full turn, so you can confirm θ = ωt against a clock. Pause freezes the disc so you can read the sector at leisure.
The misconception this lab is built to kill is the idea that a point further from the axis is somehow “spinning faster”. It is not. It is moving faster while spinning at exactly the same rate, and confusing those two is what makes rotation problems go wrong. A useful check: any answer where moving a mass outwards changes ω, T or f is an answer to a different question. For the force that holds the outer marker on its curve, the circular motion physics guide takes it further; the full derivation and worked examples live in Angular Velocity: Formula, Units and Examples.
Because angular velocity belongs to the whole disc, not to a point on it. Every part of a rigid rotating body sweeps the same angle in the same time, so they all share one value of ω, one period and one frequency. The radius slider moves the marker to a longer circular path, and since it still completes that path in the same time, it has to travel faster: v = ωr goes up while ω does not move at all. Watch the rad/s readout as you drag the radius, and you will see it sit perfectly still.
They describe the same rotation in different units. Revolutions per minute counts whole turns per minute; radians per second counts angle per second, and one full turn is 2π radians. The conversion is ω = 2π times rpm divided by 60, so 60 rpm is one turn per second, which is 2π = 6.283 rad/s. The panel prints both, and the equivalent-rpm line converts the rad/s figure straight back so you can check the arithmetic in either direction.
The period T is the time for one complete revolution, in seconds. It is the reciprocal of the rotation rate: T = 60 divided by rpm, which is the same as 2π divided by ω. Frequency f is simply 1/T, the number of turns per second, measured in hertz. Raising the rpm slider drives T down and f up together. At 1 rpm the disc takes a full 60 s per turn; at 600 rpm the period falls to 0.1 s.
Speed is linear in the rotation rate but centripetal acceleration is quadratic. Tangential speed is v = ωr, so doubling ω doubles v. Centripetal acceleration is a = ω2r, so doubling ω multiplies a by four. Double the rpm on the slider and the speed readout doubles while the acceleration readout quadruples. Reading it backwards, the rotation rate needed for a target acceleration is ω = sqrt(a / r), which is why spin-testing a component to high g-loads needs a surprisingly modest increase in rpm.
Partly. The angular frequency of a pendulum or a mass on a spring uses the same symbol ω, the same unit of rad/s, and the same links to period and frequency, so ω = 2πf and T = 2π/ω carry over exactly. What does not carry over is the geometry: an oscillator is not physically going round a circle, so there is no radius, no tangential speed and no centripetal acceleration to read off. Use the timing half of this lab for oscillations and ignore the v = ωr half.