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How It Works
Any object moving in a circle is continuously changing direction, which requires an inward (centripetal) acceleration of a = v²/r. The circular velocity equation v = 2πr/T connects speed to the radius and the time for one full revolution (the period). Both formulas can be rearranged to solve for any variable.
These relationships apply to everything from cars on a curved road to satellites in orbit. A larger radius or slower speed means less centripetal acceleration; a shorter period at the same radius means higher speed and acceleration.
Example Problem
A car travels at 20 m/s around a circular track with a radius of 50 m. What is the centripetal acceleration?
- a = v² / r = (20)² / 50 = 400 / 50
- a = 8 m/s²
The driver feels roughly 0.82 g of lateral acceleration toward the center of the track.
Frequently Asked Questions
What is centripetal acceleration?
Centripetal acceleration is the inward acceleration experienced by any object moving along a curved path. It always points toward the center of curvature and equals v²/r.
What is the difference between centripetal and centrifugal force?
Centripetal force is a real inward force that keeps an object on a curved path. Centrifugal “force” is a perceived outward push felt only inside a rotating reference frame — it is not a real force but an effect of inertia.
How do you calculate orbital period from radius?
Rearrange v = 2πr/T to get T = 2πr/v. For a satellite at r = 7,000 km with v = 7.5 km/s, T = 2π(7000)/7.5 ≈ 5,864 s (≈ 97.7 minutes).
Does mass affect centripetal acceleration?
No. Centripetal acceleration (a = v²/r) depends only on speed and radius. However, the centripetal force needed (F = ma) does depend on mass.
Related Calculators
- Gravity Equations Calculator — calculate gravitational force and orbital parameters.
- Force Equation Calculator — find the centripetal force from mass and acceleration.
- Pendulum Calculator — analyze another form of periodic motion.
- Torque Calculator — compute rotational force for spinning objects.
- Acceleration Converter — convert between m/s², ft/s², g, and other acceleration units.
Reference: Tipler, Paul A. 1995. Physics For Scientists and Engineers. Worth Publishers. 3rd ed.