Centripetal Force
Centripetal force is the net inward force that acts on an object moving in a circular path, always directed toward the center of the circle. It is not a new type of force but rather the resultant of existing forces (tension, gravity, friction, normal force) that provides the necessary centripetal acceleration. Without this inward force, an object would continue in a straight line by Newton's first law.
Key Formula
Fc = mv² / r = mrω²
LaTeX: F_c = \frac{mv^2}{r} = mr\omega^2
| Symbol | Meaning | Unit |
|---|---|---|
| F_c | Centripetal force | N |
| m | Mass of the object | kg |
| v | Linear (tangential) speed | m/s |
| r | Radius of circular path | m |
| \omega | Angular velocity | rad/s |
Worked Example
Problem
A 1.2 kg ball is swung in a horizontal circle on a string of radius 0.80 m at a speed of 4.0 m/s. Calculate the centripetal force acting on the ball.
Solution
Step 1: Identify given values — m = 1.2 kg, v = 4.0 m/s, r = 0.80 m. Step 2: Apply the formula Fc = mv²/r. Step 3: Fc = (1.2 × 4.0²) / 0.80 = (1.2 × 16) / 0.80 = 19.2 / 0.80.
Answer
Fc = 24 N, directed toward the center of the circle.
Sources of centripetal force in common circular-motion scenarios
| Scenario | Object | Radius (m) | Speed (m/s) | Providing Force |
|---|---|---|---|---|
| Car on a curve | Car (1000 kg) | 50 | 20 | Road friction |
| Satellite orbit | Satellite (500 kg) | 6,771,000 | 7,670 | Gravity |
| Ball on a string | Ball (0.5 kg) | 1.0 | 3.0 | String tension |
| Fairground ride | Rider (70 kg) | 8 | 10 | Normal force |
| Electron in atom | Electron (9.1×10⁻³¹ kg) | 5.3×10⁻¹¹ | 2.2×10⁶ | Electrostatic force |
Interactive Tools
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Related Terms
Centripetal Acceleration
Centripetal acceleration is the acceleration experienced by an object moving in a circular path, always directed toward the center of the circle. Although the object's speed may remain constant, its direction changes continuously, producing a non-zero acceleration perpendicular to the velocity. This acceleration is responsible for the continuous change in the direction of motion.
Circular Motion
Circular motion is the motion of an object along the circumference of a circle or a circular path at a constant or varying speed. In uniform circular motion, the speed is constant but the velocity vector continuously changes direction, requiring a centripetal acceleration and force directed toward the center. Circular motion is fundamental to understanding planetary orbits, rotating machinery, and many natural phenomena.
From Latin "centrum" (center) and "petere" (to seek). The term was coined by Isaac Newton in his 1684 work "De motu corporum in gyrum", meaning literally "center-seeking force".