How to play Flywheel Race
- Choose a flywheel and read the pull, the spool radius, the moment of inertia, and the target on the card.
- Find the cord's torque, τ = F·r, and subtract any bearing friction to get the net torque.
- Use τ_net = I·α with α = Δω ÷ t to find the time, the pull, or where the masses go, type it, and press Pull.
- Watch the ω–t graph: a wheel on pace reaches the target line together with the pace wheel.
What makes a wheel spin up faster?
A net force gives a body linear acceleration, F = m·a. In the same way, a net torque gives a body that can turn an angular acceleration: τ = I·α. The moment of inertia I plays the part of mass. It depends not only on how much mass there is but on where it sits: each piece counts with the square of its distance from the axis, I = Σ m·r². So the same torque spins up a wheel with its mass near the hub much faster than one with its mass out at the rim. Bearing friction gives a torque against the motion, so only the net torque speeds the wheel up. With zero net torque the wheel keeps turning at a steady speed, Newton's first law for rotation.
A focused learning model
The flywheel turns about a fixed axle. The cord pulls with a constant force tangent to the spool, so its torque F·r is constant and it never runs out. Bearing friction is a constant torque against the motion; a wheel at rest stays at rest while the cord's torque is no more than the friction. With a constant net torque, α = (τ − τ_f) ÷ I is constant, so ω = ω₀ + α·t and θ = ω₀·t + ½·α·t² are evaluated exactly, and the target speed is reached exactly at t = (ω − ω₀) ÷ α. A run ends there, or after twice the pace time. Point masses on the spokes add m·x² each. Plays in real time.