Applying Circular Motion — Quick Summary
Mr Toogood's Physics · Periodic motion
In every scenario below, the same question applies: what provides the resultant force F=mv²/r directed toward the centre of the circular path?
The bucket trick & artificial gravity
Water stays in an inverted, spinning bucket if the centripetal acceleration is at least free-fall acceleration — otherwise the water simply falls out.
The same idea creates artificial gravity in a rotating space station. Setting a = g exactly and rearranging gives the required spin rate:
Cars going over hills
Weight and support force S combine to provide the centripetal force.
On a flat road, S = mg. Going over a hill, the resultant of weight and support force provides the centripetal force:
As speed increases, S must shrink. When S reaches zero the car is airborne — this defines the maximum safe speed:
Going round banked bends
Banking lets the normal force supply some (or all) of the centripetal force.
On a flat track, friction alone provides the centripetal force. Banking the track lets the normal force N contribute too, reducing the reliance on friction. Resolving:
- Horizontal: N sinθ + F cosθ = mv²/r
- Vertical: N cosθ = mg
At one particular speed, friction isn't needed at all (F=0). Dividing the two equations gives:
Exam essentials
What supplies the force?
- Bucket / space station: the floor's push on the water/occupants.
- Car over a hill: the difference between weight and support force.
- Banked corner: components of normal force and friction.
Key results to remember
- v₀=√(gr) — max speed before a car leaves the road.
- v²=gr tanθ — no-friction speed on a banked track.
Common slips
- Resultant force always points toward the centre of the curve, not straight down.
- Use g = 9.81 m s⁻² unless told otherwise.
- Check whether the question wants the car airborne (S=0) or just "on the verge" — same condition, different wording.