Circular Motion and Centripetal Force
~8 min read
- Centripetal force: Directed toward centre. F = mv²/r = mω²r. Without it, body flies off tangentially.
- Centrifugal force: Pseudo-force in the rotating frame, equal and opposite to centripetal.
- Examples: Planets around the Sun, satellites, vehicle on curved road, washing machine spin-dryer.
Any body moving in a circle must be pulled toward the centre by a real force. CDS/OTA tests its direction, formula and everyday applications like banking of roads and satellite motion.
Uniform Circular Motion
- Speed is constant; velocity changes direction continuously.
- Therefore the body has centripetal acceleration a = v²/r = ω²r — always directed toward the centre.
- Angular velocity ω = v/r = 2π/T (T = period).
- Frequency f = 1/T. ω = 2πf.
- Required centripetal force F = mv²/r.
Centrifugal Force (Pseudo)
- Felt only in a rotating (non-inertial) frame.
- Acts radially outward — opposite to centripetal.
- Not a real force; it is the inertia of the moving body as seen from the rotating frame.
- Used in centrifuges to separate dense and light components (cream from milk, blood plasma, uranium isotopes).
Everyday Applications
| Situation | Centripetal force is provided by |
|---|---|
| Stone tied to string whirled in circle | Tension in the string |
| Car on flat curve | Friction between tyres and road |
| Car on banked road | Horizontal component of normal reaction |
| Earth-Moon, Sun-Earth | Gravitational attraction |
| Electron in atom (Bohr model) | Electrostatic attraction by nucleus |
Banking of roads: outer edge raised so that the horizontal component of normal reaction provides centripetal force, reducing dependence on friction.
CDS/OTA PYQ Examples
Q: A car takes a circular turn. Centripetal force is provided by:
(a) Gravity (b) Friction between tyres and road (c) Engine torque (d) Air drag
Answer: (b) Friction (on a flat road).
Q: In uniform circular motion, which quantity remains constant?
(a) Velocity (b) Acceleration (c) Speed (d) Centripetal force direction
Answer: (c) Speed — direction of velocity changes.
Q: Centripetal acceleration is directed:
(a) Along motion (b) Opposite to motion (c) Towards centre (d) Away from centre
Answer: (c) Towards centre.
Q: A cream separator works on the principle of:
(a) Capillary action (b) Centrifugal action (c) Surface tension (d) Viscosity
Answer: (b) Centrifugal action — denser water moves out, lighter cream remains near axis.
Drill Circular Motion and Centripetal Force for CDS/OTA
CDS/OTA-pattern items on Circular Motion and Centripetal Force with answer keys and explanations.
Start Free Mock TestFrequently Asked Questions
Why does water not fall when a bucket is whirled vertically?
At the top of the loop, gravity provides the centripetal force. So long as speed is high enough that mg ≤ mv²/r, the water keeps pressing against the bucket bottom.
Why are roads banked at curves?
To reduce reliance on friction. The horizontal component of the normal reaction provides centripetal force, so vehicles can negotiate the curve safely even on slippery surfaces.
Is centrifugal force a real force?
No. It is a pseudo-force that appears only in a rotating frame of reference, used to make Newton's laws work there.