Calculate centripetal force for objects in circular motion using Fc = mv²/r. Determine centripetal force from mass, velocity, and radius with step-by-step physics solutions for circular motion problems.
Problem: A 1200 kg car travels around a circular curve with a radius of 50 m at a speed of 15 m/s. What centripetal force is required to keep it on the curve?
Solution: Using Fc = mv²/r
Fc = (1200 × 15²) / 50 = (1200 × 225) / 50 = 270,000 / 50 = 5,400 N
This force is provided by the friction between the car's tires and the road surface. If the road is icy and friction is insufficient, the car will skid outward.
Problem: A 500 kg satellite orbits Earth at an orbital radius of 7,000 km from Earth's center with a velocity of 7,500 m/s. What centripetal force acts on it?
Solution: Using Fc = mv²/r
Fc = (500 × 7500²) / (7000 × 1000) = (500 × 56,250,000) / 7,000,000 = 4,017.86 N
This centripetal force is provided entirely by Earth's gravitational pull. The satellite is in free fall toward Earth, but its tangential velocity keeps it in orbit.
Problem: An amusement park ride spins riders in a horizontal circle of radius 6 m. A rider with mass 75 kg experiences a centripetal force of 1800 N. What is their speed?
Solution: Using v = √(Fc·r/m)
v = √(1800 × 6 / 75) = √(10,800 / 75) = √144 = 12 m/s
At 12 m/s (about 43 km/h), the rider experiences a centripetal acceleration of 2.45 g's — more than twice the force of gravity pushing them against the wall.
Problem: A 0.15 kg ball is swung in a horizontal circle with a radius of 1.2 m at a speed of 8 m/s. What is the tension (centripetal force) in the string?
Solution: Using Fc = mv²/r
Fc = (0.15 × 8²) / 1.2 = (0.15 × 64) / 1.2 = 9.6 / 1.2 = 8 N
The tension in the string provides the centripetal force. If the string can only withstand 10 N, the ball must be kept below approximately 8.94 m/s to avoid breaking the string.
Where Fc is centripetal force (N), m is mass (kg), v is velocity (m/s), and r is radius of curvature (m).
Centripetal acceleration is related to force by Fc = m × ac. You can also express it in g-force by dividing by 9.81 m/s².
Centripetal force is the inward force required to keep an object moving in a circular path. It always points toward the center of rotation. Despite common misconceptions, there is no "centrifugal force" pushing outward — what you feel is inertia trying to keep you moving in a straight line.
Fc = mv²/r shows that force increases with mass and the square of velocity, but decreases with larger radius. Doubling the velocity quadruples the required force — this is why sharp turns at high speed are so dangerous.
"Centripetal" means "center-seeking" — the real inward force. "Centrifugal" means "center-fleeing" — a fictitious force experienced in a rotating reference frame. In an inertial frame, only centripetal force exists. The "centrifugal" feeling is actually your body's inertia resisting the change in direction.
Centripetal force is essential in countless applications: car turns (friction), satellite orbits (gravity), roller coaster loops (normal force), centrifuges (artificial gravity), washing machine spin cycles, and particle accelerators (magnetic fields).
⚠️ Important Note: This calculator assumes ideal circular motion with constant speed. Real-world scenarios may involve additional forces such as friction, air resistance, gravity, or non-uniform motion. Centripetal force is not a separate force — it is the net force directed toward the center of the circular path. Always ensure the physical source of centripetal force (tension, friction, gravity, normal force) is adequate for the required force.
Centripetal force is a fundamental concept in classical mechanics that describes the inward force required to keep an object moving in a curved or circular path. Without a centripetal force, an object in motion would continue in a straight line due to inertia — this is Newton's first law of motion in action.
When an object moves in a circle, its velocity vector is constantly changing direction (though its speed may be constant). A change in direction constitutes acceleration, and according to Newton's second law (F = ma), any acceleration requires a net force. For circular motion, this net force is called centripetal force, and it always points toward the center of the circle.
The magnitude of the centripetal acceleration is ac = v²/r, meaning it increases with the square of the velocity and decreases with larger radius. The corresponding centripetal force is Fc = mv²/r, which also depends linearly on mass.
When a car goes around a curve, the friction between the tires and the road provides the centripetal force. The maximum safe speed for a curve depends on the radius of the curve and the coefficient of friction. Banked curves use the normal force component to supplement friction, allowing higher safe speeds. Formula: vmax = √(μgr) for flat curves, where μ is the friction coefficient.
Satellites remain in orbit because Earth's gravity provides exactly the centripetal force needed for their circular (or elliptical) path. The orbital velocity for a circular orbit is v = √(GM/r), where G is the gravitational constant and M is the mass of the central body. At this velocity, the gravitational force equals the required centripetal force, creating a stable orbit.
Centrifuges use rapid rotation to create large centripetal forces, effectively creating an enhanced gravitational field. This allows separation of mixtures by density — denser particles experience a greater net inward force and move outward (radially) in the rotating frame. Biological centrifuges can generate forces of 10,000 g or more.
Roller coasters, spinning rides, and centrifugal force rides all rely on centripetal force principles. The famous "wall of death" ride pins riders against a rotating wall — the normal force from the wall provides the centripetal force. The minimum speed to prevent sliding down is vmin = √(gr/μ).
The centripetal force needed for circular motion increases with the square of velocity. Going twice as fast around the same curve requires four times the centripetal force.
A person standing on Earth's equator is moving at about 465 m/s (1,674 km/h) due to Earth's rotation. The centripetal force required is about 0.34% of their weight — this tiny fraction of gravity is "used up" for circular motion, making them slightly lighter than at the poles.