Rotation and angular momentum
Predict firstWhich moves faster: a point near the axis or a point near the rim?
Distinguish speed, momentum, torque and energy by changing physical apparatus.
Prerequisites: No formula is needed to begin. One revolution is 2π radians; angular speed ω is radians per second. Moment of inertia I depends on mass and its distance from the axis.First, watch a real rotation
Predict firstWhich moves faster: a point near the axis or a point near the rim?
Play and watch the central reel and the end marker. Both finish a turn together, so their angular speeds match. The outer point covers a longer distance each turn, so its linear speed v = rω is larger. Positive rotation here means clockwise viewed from above. The right rotor keeps its initial mass distribution throughout.
How to observe
- Compare moving and fixed weights: connect radius, angular speed and energy.
- Use identical hanging masses to drive a solid disk and a thick annulus.
- Bring two rotors into contact and follow spin transfer and frictional heating.
Model notes
Classical rotation about a fixed vertical axis. Experiment 1 accounts for the left rotor and actuator; the right is an independent reference. Finite cylindrical weights and radial kinetic energy are included. Experiment 2 compares a uniform disk and thick annulus with equal mass and outer radius; hub, spokes, string and pulley inertia are neglected. Bearings are frictionless; the taut inextensible string does not slip. Both runs end at the same physical time, before impact with the floor. Experiment 3 uses equal-inertia rotors and gradually engaged dry friction, followed by static locking; only rotational energy is accounted for, not the axial placement work. Cyan, violet and amber encode rotational kinetic energy, gravitational potential and frictional dissipation, not literal glow or measured temperature. Gyroscopic precession, elastic vibration and air drag are outside this model.