Physics Classical Mechanics • Angular Momentum
Model the ice-skater effect using conservation of angular momentum: \[ I_i\omega_i=I_f\omega_f. \] When the skater pulls their arms inward, \(I\) decreases and \(\omega\) increases. The calculator finds final angular velocity, inertia change, angular momentum, and energy change.
The ice skater effect is the increase in spin rate when a skater pulls their arms inward, decreasing moment of inertia while angular momentum remains conserved.
The main formula is Ii omega_i = If omega_f. Solving gives omega_f = (Ii / If) omega_i.
Pulling arms inward decreases the skater's moment of inertia. Since angular momentum L = I omega is conserved, angular velocity omega increases.
Extending the arms outward increases moment of inertia, so angular velocity decreases if angular momentum is conserved.
Not necessarily. Angular momentum is conserved if external torque is negligible, but kinetic energy can change because the skater does work with their muscles.
A 40% decrease means If = 0.60 Ii. Therefore omega_f = 2 / 0.60 = 3.33 rad/s.
A negative percent decrease means the final moment of inertia is larger than the initial moment of inertia.
Yes. If the initial and final angular velocities are known, it can solve the percent inertia change needed to conserve angular momentum.
The SI unit of angular momentum is kg m^2/s.
The animation shows a skater changing arm span while the spin speed updates to keep angular momentum conserved.