1.5 Effects of Forces – Circular Motion (Supplement 12)
Key Idea
When a force acts radially inward, i.e. perpendicular to the instantaneous direction of motion, it does not change the object's speed directly.
Instead it supplies the centripetal force that continually changes the direction of the velocity, keeping the object on a circular path.
Syllabus‑aligned qualitative statements
For the four quantities – mass \(m\), speed \(v\), radius \(r\) and required inward force \(F\) – the Cambridge IGCSE 0625 specification expects the following qualitative relationships:
- Speed increases if the inward force increases, with mass and radius kept constant.
- Radius decreases if the inward force increases, with mass and speed kept constant.
- Required inward force increases if the mass increases, with speed and radius kept constant.
Quick Reference Table (ordered as in the syllabus)
| Quantity that is increased | Other quantities kept constant | Resulting change | Everyday illustration |
|---|
| Inward force \(F\) ↑ | Mass \(m\) and radius \(r\) fixed | Speed \(v\) ↑ | Pulling a stone on a string tighter makes it whirl faster around the same circle. |
| Inward force \(F\) ↑ | Mass \(m\) and speed \(v\) fixed | Radius \(r\) ↓ (path becomes tighter) | Increasing tyre grip (more friction) lets a car take a sharper bend at the same speed. |
| Mass \(m\) ↑ | Speed \(v\) and radius \(r\) fixed | Required inward force \(F\) ↑ | A heavier satellite needs a stronger gravitational pull to stay in the same orbit. |
Qualitative Explanations (in syllabus order)
- Increasing the inward force while \(m\) and \(r\) are unchanged makes the speed increase.
- The force remains directed toward the centre, i.e. perpendicular to the motion.
- To stay on the same circular path, a larger inward pull must be balanced by a larger tangential speed (since \(F\propto v^{2}\) for fixed \(m\) and \(r\)).
- Example: A ball on a string is swung in a horizontal circle. Pulling the string a little tighter (greater \(F\)) makes the ball speed up while the radius stays the same.
- Increasing the inward force while \(m\) and \(v\) are unchanged makes the radius decrease.
- The object continues to move at the same speed, but the stronger inward pull bends its path more sharply.
- Since \(F\propto 1/r\) for fixed \(m\) and \(v\), a larger \(F\) must be accompanied by a smaller \(r\).
- Example: A cyclist leans into a curve. If the friction between tyre and road is increased (greater \(F\)), the cyclist can follow a tighter (smaller‑radius) turn at the same speed.
- Increasing the mass while \(v\) and \(r\) are unchanged requires a larger inward force.
- A heavier object possesses more inertia; a stronger inward pull is needed to keep it on the same circular path.
- Because \(F\propto m\) for fixed \(v\) and \(r\), the required force rises in direct proportion to the mass.
- Example: A satellite with double the mass needs twice the gravitational attraction to remain in the same orbit.
Assumptions for the qualitative statements
- Only the quantity mentioned is varied; all other relevant quantities are held constant.
- The inward force is always radial (perpendicular to the instantaneous velocity).
- Air resistance, buoyancy and other external forces are ignored.
Common sources of the inward (centripetal) force
- Friction between tyres and road (vehicle cornering).
- Tension in a string or rope (stone‑whirling experiment).
- Gravitational attraction (planetary or satellite orbits).
- Normal reaction on a banked track or roller‑coaster track.
Optional extension – the quantitative relation
Although not required for the IGCSE exam, the relationship can be written as
\(F = \dfrac{mv^{2}}{r}\)
Re‑arranging this equation reproduces the three qualitative cases above, reinforcing the direction of the relationships.
Suggested diagram (teacher‑drawn or worksheet illustration)
- Top‑view of a circle with an object on the perimeter.
- Three labelled sketches (a), (b) and (c):
- (a) Same radius, larger speed – longer tangent arrow \(v\), same radial arrow \(F\).
- (b) Same speed, smaller radius – same length tangent arrow \(v\), longer radial arrow \(F\).
- (c) Same speed and radius, larger mass – same arrows as (b) but a note “larger \(m\) → larger required \(F\)”.
- All arrows should be clearly marked: v (tangential, clockwise) and F (radial, pointing to the centre).
Key Points to Remember
- The centripetal force is always perpendicular to the direction of motion.
- Changing the magnitude of that force changes either the speed or the radius, depending on which other quantity is held constant.
- Heavier objects require a larger inward force to maintain the same circular motion.
- Real‑world examples – car cornering, stone‑whirling, satellite orbits – illustrate these qualitative relationships without the need for calculations.