Centripetal Force Calculator

What is Centripetal Force & Acceleration?

Any object moving in a circular path requires a centripetal ("center-seeking") force directed inward toward the center of the circle. Without this force, the object would travel in a straight line per Newton's First Law. Centripetal force is not a new type of force — it is always provided by an existing physical force such as gravity (orbits), friction (cars turning), or tension (ball on a string).

Mathematical Foundation

F_c = \frac{mv^2}{r}

F_c

= Centripetal force in Newtons (N) — the net inward force required to maintain circular motion.

m

= Mass of the rotating object in kilograms (kg).

v

= Tangential (linear) velocity in meters per second (m/s). Note: velocity is squared, so doubling speed quadruples the force.

r

= Radius of the circular path in meters (m). Larger radius = less force needed at the same speed.

a_c = \frac{v^2}{r}

a_c

= Centripetal acceleration in m/s². Divide by 9.80665 to convert to g-force.

Laws & Principles

Centripetal ≠ Centrifugal: Centrifugal force is a fictitious (pseudo) force that only appears in the rotating reference frame. In an inertial frame, the only real force is centripetal — always pointing inward. Never draw centrifugal force on a free-body diagram.
v² Scaling Law: Because velocity is squared, doubling the speed of a car in a turn requires 4× the friction force. This is why highway exit ramp speed limits drop dramatically for tight curves.
Derived Quantities: Period T = 2πr/v (time for one revolution). Angular velocity ω = v/r (radians per second). g-Force = a_c / 9.80665.

Step-by-Step Example Walkthrough

" A 1,500 kg car takes a curve of radius 50 m at 20 m/s (72 km/h). "

1. Calculate centripetal acceleration: a_c = v²/r = (20)²/50 = 400/50 = 8.0 m/s².
2. Convert to g-force: 8.0 / 9.81 = 0.82g.
3. Calculate centripetal force: F_c = m × a_c = 1500 × 8.0 = 12,000 N.
4. Calculate period: T = 2π(50)/20 = 15.7 seconds per revolution.

Final Result: The tires must provide 12,000 N (0.82g) of lateral friction to keep the car on the road. On wet pavement (μ ≈ 0.4), the maximum friction is only 5,886 N — the car would skid off the road at this speed.

Quick Answer: What is Centripetal Force?

Centripetal force is the net inward force required to keep an object moving in a circle instead of flying off in a straight line. The formula is F_c = mv²/r, where m is mass (kg), v is tangential velocity (m/s), and r is the radius of the circular path (m). The force always points toward the center of the circle. It is not a new type of force — it is always provided by an existing force (gravity for orbits, friction for cars turning, tension for a ball on a string).

Centripetal Force in Real-World Scenarios

Every circular motion in nature and engineering requires a centripetal force. Understanding which physical force provides the centripetal acceleration is the key insight for solving circular motion problems.

Scenario	What Provides the Centripetal Force	Typical g-Force
Car turning on a road	Static friction between tires and pavement	0.3-0.8g
Roller coaster loop	Normal force from track + gravity	3-6g
Moon orbiting Earth	Gravitational attraction	0.0027g
Fighter jet in a turn	Aerodynamic lift force tilted inward	6-9g
Washing machine spin cycle	Drum wall normal force	300-500g

Pro Tips & Common Physics Mistakes

Do This

✓Remember that velocity is squared. Doubling the speed quadruples the centripetal force. This is why highway exit ramp speed limits drop dramatically for tight radius curves — even a small speed increase produces an exponentially larger force that can exceed the tire's friction limit.
✓Convert RPM to m/s before using the formula. If you know rotational speed in RPM, convert to tangential velocity: v = 2πr × (RPM/60). The formula F = mv²/r requires tangential velocity in m/s, not angular velocity.

Avoid This

✗Don't call it "centrifugal force." Centrifugal force is a fictitious (pseudo) force that only exists in the rotating reference frame. The real physics is centripetal — always pointing inward. When you feel "pushed outward" on a merry-go-round, your body is actually trying to travel in a straight line (Newton's 1st Law) while the floor pushes you inward.
✗Don't treat centripetal force as a separate force in free-body diagrams. It is the net result of all real forces pointing toward the center. On a banked curve, centripetal force = component of normal force + component of friction. Drawing "F_c" as a separate arrow is a common exam mistake.

Frequently Asked Questions

What is the difference between centripetal and centrifugal force?

Centripetal force is real — it points inward toward the center of the circle and is provided by friction, gravity, tension, or another physical force. Centrifugal force is fictitious — it only appears when you analyze motion from within the rotating reference frame. In an inertial (non-rotating) reference frame, centrifugal force does not exist.

How many g's can a human survive?

Sustained g-forces above 5g cause vision narrowing ("greyout") and above 9g cause unconsciousness (G-LOC). Fighter pilots wearing G-suits can tolerate up to 9g for short durations. The record for survived g-force is 46.2g (John Stapp's rocket sled test in 1954). Roller coasters typically max at 3-5g, and NASCAR crashes have been recorded above 70g for milliseconds.

Why do objects fly off tangentially, not radially outward?

When the centripetal force is removed (string breaks, car hits ice), the object continues in the direction it was already moving — which is tangent to the circle at that instant, not radially outward. This is Newton's First Law: an object in motion continues in a straight line unless acted upon by a force. It only "appears" to fly outward because of the observer's rotating reference frame.

Centripetal Force Calculator

Centripetal Force Calculator

Physics: Centripetal Force

F_c = mv²/r