What Is Centripetal Force?
Centripetal force is the net force directed toward the centre of a circular path that keeps an object moving in a circle. Without it, the object would travel in a straight line (Newton’s first law). It’s not a new kind of force — it’s provided by real forces like gravity, tension, or friction.
Circular Motion
F = mv²/r
This relates the centripetal force to the mass, speed, and radius of the circular path. Doubling the speed quadruples the required force.
F = mrω² (Angular Velocity Form)
Using angular velocity ω (rad/s) instead of linear speed. Useful for rotating machinery, centrifuges, and orbital calculations. Convert RPM to ω: ω = RPM × 2π/60.
Centripetal vs Centrifugal Force
Centripetal = real inward force (exists in all reference frames).
Centrifugal = fictitious outward force (only appears in a rotating reference frame). When you feel “pushed outward” on a merry-go-round, that’s the centrifugal effect in your rotating frame.
Banked Curves
Ideal Banking Angle
Max Speed (Flat Curve)
On a frictionless banked curve, the normal force provides all the centripetal force. The ideal banking angle depends only on speed, radius, and gravity. On a flat curve, friction alone provides centripetal force, limiting the maximum safe speed.
Real highway curves use a combination of banking and friction. The banking angle typically ranges from 2° to 10° on roads, and up to 33° on NASCAR tracks.
Applications of Centripetal Force
| Application | Source of Fᴄ | Typical values |
|---|---|---|
| Car on curve | Friction + banking | 3,000–15,000 N |
| Satellite in orbit | Gravity | ~3,500 N (ISS per kg) |
| Centrifuge | Normal force (tube wall) | Up to 900,000× g |
| Roller coaster loop | Normal + gravity | 2–5 g |
| Washing machine | Drum wall | 300–500 g |
How to Use the Calculator
- Choose a calculation mode for your known quantities.
- Enter values with units.
- Click Calculate.
- Review force, acceleration, speed, and radius results.
Example Calculations
Car: 1500 kg, 20 m/s, r = 50 m
F = 1500 × 400 / 50 = 12,000 N = 12 kN
Ball on string: 0.5 kg, 3 m/s, r = 1 m
F = 0.5 × 9 / 1 = 4.5 N
Centrifuge: 0.01 kg, r=0.1 m, 3000 RPM
ω = 3000 × 2π/60 = 314.2 rad/s; F = 0.01 × 0.1 × 314.2² ≈ 98.7 N
Common Mistakes
- Thinking centripetal force is a separate force (it’s the net radial force).
- Confusing centripetal (inward) with centrifugal (outward, fictitious).
- Using diameter instead of radius.
- Forgetting to convert RPM to rad/s before applying the formula.
Accuracy and Limitations
These formulas assume uniform circular motion (constant speed). For non-uniform circular motion, tangential acceleration must also be considered. The calculator does not account for air drag, friction losses, or elastic effects. Results are for education and estimation.
FAQ
What is centripetal force?›
It’s the net inward force required to keep an object moving along a curved path. For a car on a curve, friction provides it; for a satellite, gravity provides it.
Is centrifugal force real?›
Centrifugal force is a fictitious (pseudo) force that appears in a rotating reference frame. In an inertial frame, only centripetal force exists.
What provides centripetal force?›
Any real force can act as centripetal force: gravity (orbits), tension (ball on a string), friction (car on a curve), normal force (loop-the-loop).
Does centripetal force do work?›
No. Centripetal force is always perpendicular to velocity, so it does zero work. It changes direction, not speed.
How do I convert RPM to angular velocity?›
ω = RPM × 2π/60 rad/s. For example, 60 RPM = 2π rad/s ≈ 6.28 rad/s.
What happens if centripetal force is removed?›
The object moves in a straight line tangent to the circle (Newton’s first law). It does not fly outward.
What is the banking angle for a curve?›
For a frictionless banked curve: tanθ = v²/(rg). At the ideal angle, no friction is needed. Real roads combine banking with friction for safety across a range of speeds.
What is the maximum speed on a flat curve?›
v = √(μgr), where μ is the friction coefficient, g is gravity, and r is the curve radius. Wet roads (μ ≈ 0.4) have much lower limits than dry roads (μ ≈ 0.7–0.8).
Sources
Author & technical reviewer
Manish Kumar
PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.
Learn more about Manish