A.4 · IB Physics
Rolling down a slope
Race a hoop, a disc, a solid sphere and a block sliding without friction down the same slope. The rolling objects must put part of their energy into rotation, so the bigger the rotational share, the slower the object.
Predict first
Start from the default settings on Earth. If you change the gravitational field strength g to the Moon, about how much longer does the hoop take to reach the bottom?
From L = ½at² with a = g sinθ ÷ 2, t is proportional to 1 ÷ √g. Since 9.81 ÷ 1.62 ≈ 6.06, the time increases by about √6.06 ≈ 2.46.
Check it in the model: Press Race and note the hoop time, then choose Moon in the Gravitational field strength, g list, press Race again and compare.
objects: hoop disc solid sphere block
mgh = ½mv² + ½Iω² = ½mv²(1 + I ÷ mr²)
a = g sinθ ÷ (1 + I ÷ mr²)
I ÷ mr²: hoop 1, disc ½, sphere ⅖, block 0
μ ≥ tanθ × (I ÷ mr²) ÷ (1 + I ÷ mr²)
Try this
- Press Race with the default settings. Predict the finishing order first, then match each time to a = g sinθ ÷ (1 + I ÷ mr²).
- Change the mass from 1.0 kg to 5.0 kg and the radius from 0.10 m to 0.30 m. Which finishing times change, and why?
- Choose the Moon, then compare the hoop and the block. Does the ratio of their finishing times change, and what does the μ readout say about a gentle slope compared with a steep one?
Common error: thinking friction wastes energy on a rolling object: with no slipping the contact point is at rest, static friction does no work, and mechanical energy is conserved. Friction only supplies the torque, shifting energy into rotation, which is why rolling is slower than sliding.