Unit 6 Games
Four games, each with levels from easy to hard and a score. Your best score for each level is saved on this device. Everything works with a mouse, a finger or the keyboard (Tab to move, Enter or Space to press, arrow keys on sliders). Back to the Unit 6 overview or on to the practice set.
1. Rolling race: which one wins?
Objects start from rest at the top of the same ramp and roll without slipping. Pick the winner (or the loser, when the level asks), then press Race to see if you were right. Hint: the smaller the share of energy that goes into spin, the faster the object.
2. Skater spin challenge
The skater spins with her arms out. No outside torque acts, so her angular momentum L = Iω stays the same. Choose where her hands end up (the arm radius r) so that she spins at the target rate. Her body has rotational inertia Ibody, and each hand plus arm acts like a small mass m at distance r, so I = Ibody + 2mr².
3. Orbit launcher
A rocket carries a satellite up and then pushes it sideways (horizontally). Set the launch value and press Launch. Use G = 6.67 × 10⁻¹¹ N·m²/kg², Earth mass 5.97 × 10²⁴ kg, Earth radius 6370 km. Remember r is measured from Earth's center: r = 6370 km + altitude.
4. Energy bar puzzle: rolling
Set the three energy bars for the moment shown, as a percentage of the total energy of the object-Earth system. U is gravitational potential energy (zero at the bottom), Ktrans = ½Mv², Krot = ½Iω². No slipping, no air drag. The shape tells you β in I = βMR², and for rolling Krot/Ktrans = β.