🌀 Centripetal Force Calculator
Calculate centripetal force
How to Use This Calculator
Enter Mass
Input the mass (m) of the object in kilograms (kg). This is the mass of the object moving in a circular path. For example, a 1 kg ball on a string or a 1500 kg car going around a curve.
Enter Velocity
Input the tangential velocity (v) in meters per second (m/s). This is the speed of the object as it moves along its circular path. Make sure this is the linear speed, not angular velocity. For example, a car going 20 m/s around a curve.
Enter Radius
Input the radius (r) in meters (m). This is the distance from the center of the circular path to the object. The radius must be positive and greater than zero. This value cannot be zero.
Calculate and Review
Click the "Calculate Centripetal Force" button to compute the result. The centripetal force will be displayed in newtons (N). The calculator also shows the centripetal acceleration, which is the acceleration toward the center of the circle.
Formula
F = mv² / r
a = v² / r
Where:
• F = Centripetal force (N)
• m = Mass (kg)
• v = Tangential velocity (m/s)
• r = Radius (m)
• a = Centripetal acceleration (m/s²)
Example 1: Car on a Curve
A 1500 kg car travels at 25 m/s around a curve with radius 50 m. Calculate the centripetal force required.
Given:
• Mass (m) = 1500 kg
• Velocity (v) = 25 m/s
• Radius (r) = 50 m
Solution:
F = mv² / r
F = 1500 × 25² / 50
F = 1500 × 625 / 50
F = 937,500 / 50
F = 18,750 N
Centripetal acceleration: a = 25² / 50 = 12.5 m/s²
Example 2: Ball on a String
A 0.5 kg ball attached to a string moves in a circle of radius 2 m at 10 m/s. What is the centripetal force?
Given:
• Mass (m) = 0.5 kg
• Velocity (v) = 10 m/s
• Radius (r) = 2 m
Solution:
F = mv² / r
F = 0.5 × 10² / 2
F = 0.5 × 100 / 2
F = 25 N
This is the tension in the string providing the centripetal force.
Frequently Asked Questions
What is centripetal force?
Centripetal force is the force that keeps an object moving in a circular path. It always points toward the center of the circle and is required to maintain circular motion at constant speed. Without centripetal force, objects would move in straight lines (Newton's first law).
What provides centripetal force in real situations?
Centripetal force can be provided by various sources: tension (ball on a string), friction (car on a road), gravity (planets orbiting the sun), normal force (roller coaster on a loop), or any combination of forces. It's not a separate force but rather the net force pointing toward the center.
What's the difference between centripetal and centrifugal force?
Centripetal force is the real, inward-pointing force that keeps objects in circular motion (it exists in all reference frames). Centrifugal force is an apparent outward force that appears in rotating (non-inertial) reference frames. They have equal magnitude but opposite directions. Centripetal force is what actually keeps you moving in a circle, while centrifugal force is what you "feel" pushing outward.
How does velocity affect centripetal force?
Centripetal force is proportional to the square of velocity (F ∝ v²). This means doubling the velocity quadruples the centripetal force required. For example, if a car doubles its speed around a curve, it needs four times the friction force to stay on the road. This is why high-speed turns are dangerous.
What happens if centripetal force is removed?
If centripetal force is suddenly removed, the object will continue moving in a straight line tangent to the circle at the point where the force was removed (Newton's first law). For example, if a string breaks while swinging a ball, the ball flies off in a straight line, not outward.
Where is centripetal force used in real-world applications?
Centripetal force is crucial in: designing roads and banking angles for safe turns, understanding planetary motion and satellite orbits, designing roller coasters and amusement park rides, analyzing the motion of particles in accelerators, understanding the forces in washing machines and centrifuges, and designing rotating machinery and engines.
About Centripetal Force Calculator
The centripetal force calculator computes the force required to keep an object moving in a circular path at constant speed. Centripetal force is a fundamental concept in circular motion, essential for understanding everything from cars turning corners to planets orbiting the sun.
This calculator is essential for students studying circular motion, engineers designing roads and vehicles, and anyone analyzing rotational systems. Understanding centripetal force helps explain why objects stay in circular paths and what forces are needed to maintain that motion.